Compound Interest — Extra Practice

Competitive Mathematics · Arithmetic

6 Part13 worked examples129 practice questions

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

Suppose you keep ₹10,000 in a bank that pays 10% a year. With simple interest you get ₹1,000 every year. With compound interest after year one the interest of ₹1,000 joins your money, making ₹11,000; year two’s interest is on ₹11,000, i.e. ₹1,100 — the interest itself starts earning. That is “interest on interest”, and it grows faster and faster with time.

∑ Formula

A = P (1 + \frac{R}{100})^{n}, C I = A - P

The core formula for annual compounding

The formula and its uses

Finding any one of

A

P

R

n

Finding the amount, the compound interest, the principal, the rate and the time.

Annual compounding

One multiplier per year

Multiplying by $1 + \frac{R}{100}$ , $n$ times, and the reverse questions.

Factor	Rate $R$	2-year factor	3-year factor
1.05	5%	1.1025	1.157625
1.10	10%	1.21	1.331
1.20	20%	1.44	1.728
1.25	25%	1.5625	1.953125
1.04	4%	1.0816	1.124864

MemoryLearn these factors:

1. 1^{2} = 1.21

1. 1^{3} = 1.331

1. 2^{2} = 1.44

1. 2^{3} = 1.728

1.0 5^{2} = 1.1025

. Most exam questions rest on them.

Example 1 · Basic

Find the amount and the compound interest on ₹10,000 at 10% per annum for 3 years.

Solution, step by step

1 $A = 10000 \times (1.1)^{3} = 10000 \times 1.331 = 13310$ .
2 $C I = 13310 - 10000 = 3310$

Answer ₹13,310 and ₹3,310

Example 2 · Standard

A sum amounts to ₹6,760 in 2 years at 4% compound interest per annum. What was the sum?

Solution, step by step

1 $P = \frac{6760}{( 1.04 ) ^{2}} = \frac{6760}{1.0816}$ .
2 $= 6250$

Answer ₹6,250

Example 3 · Standard

₹2,500 becomes ₹2,809 in 2 years at compound interest. What is the rate per annum?

Solution, step by step

1 $(1 + \frac{R}{100})^{2} = \frac{2809}{2500} = 1.1236$ .
2 $1.1236 = 1.06$ ⟹ $R = 6%$

Answer 6%

BasicTry it yourself first

What is the amount on ₹8,000 after 2 years at 5% compound interest per annum?

BasicTry it yourself first

What is the amount on ₹5,000 after 2 years at 10% compound interest per annum?

StandardTry it yourself first

What is the amount on ₹12,500 after 3 years at 4% compound interest per annum?

BasicTry it yourself first

What is the compound interest on ₹4,000 at 10% per annum for 2 years, compounded annually?

StandardTry it yourself first

What is the compound interest on ₹25,000 at 12% per annum for 2 years, compounded annually?

StandardTry it yourself first

What is the compound interest on ₹16,000 at 5% per annum for 3 years, compounded annually?

AdvancedTry it yourself first

What is the compound interest on ₹50,000 at 20% per annum for 3 years, compounded annually?

BasicTry it yourself first

A sum amounts to ₹6,050 in 2 years at 10% compound interest per annum. What was the sum?

StandardTry it yourself first

A sum amounts to ₹8,820 in 2 years at 5% compound interest per annum. What was the sum?

AdvancedTry it yourself first

A sum amounts to ₹14,060.8 in 3 years at 4% compound interest per annum. What was the sum?

BasicTry it yourself first

₹2,500 becomes ₹2,704 in 2 years at compound interest. What is the rate per annum?

StandardTry it yourself first

₹4,000 becomes ₹4,840 in 2 years at compound interest. What is the rate per annum?

AdvancedTry it yourself first

₹8,000 becomes ₹9,261 in 3 years at compound interest. What is the rate per annum?

StandardTry it yourself first

In how many years will ₹5,000 become ₹6,655 at 10% compound interest per annum?

AdvancedTry it yourself first

In how many years will ₹2,000 become ₹3,456 at 20% compound interest per annum?

Half-yearly, quarterly and varying rates

Half the rate, twice the periods

When compounding happens more than once a year, the time has a fraction, or the rate differs each year.

Compounding	Rate per period	Periods (in $n$ years)
annual	$R$	$n$
half-yearly	$\frac{R}{2}$	$2 n$
quarterly	$\frac{R}{4}$	$4 n$

A fractional year (say 2 years 4 months): compound for the whole years, then charge simple interest on that amount for the leftover months.
A different rate each year: its own factor each year, all multiplied: $A = P (1 + \frac{R _{1}}{100}) (1 + \frac{R _{2}}{100}) \dots$ .

Example 4 · Standard

Find the quarterly compound interest on ₹8,000 at 20% per annum for 9 months.

Solution, step by step

1Rate per quarter $= 5%$ , periods $= 3$ .
2 $A = 8000 \times 1.0 5^{3} = 9261$ ⟹ $C I = 1261$

Answer ₹1,261

Example 5 · Standard

What will ₹6,000 amount to in 3 years at 5%, 10% and 20% in successive years?

Solution, step by step

1Factor $1.05 \times 1.10 \times 1.20 = 1.386$ .
2 $A = 6000 \times 1.386 = 8316$

Answer ₹8,316

BasicTry it yourself first

What is the half-yearly compound interest on ₹10,000 at 20% per annum for 1 year?

StandardTry it yourself first

What is the half-yearly compound interest on ₹16,000 at 20% per annum for 1.5 years?

StandardTry it yourself first

What is the half-yearly compound interest on ₹16,000 at 10% per annum for 2 years?

AdvancedTry it yourself first

What is the quarterly compound interest on ₹32,000 at 20% per annum for 0.75 years?

StandardTry it yourself first

What is the interest on ₹5,000 at 10% per annum compounded annually for 2 years 6 months? (Simple interest on the part year.)

AdvancedTry it yourself first

What is the interest on ₹8,000 at 10% per annum compounded annually for 1 years 9 months? (Simple interest on the part year.)

BasicTry it yourself first

₹5,000 is invested at compound interest with rates of 10%, 20% in successive years. What is the final amount?

StandardTry it yourself first

₹10,000 is invested at compound interest with rates of 5%, 10%, 20% in successive years. What is the final amount?

AdvancedTry it yourself first

₹8,000 is invested at compound interest with rates of 25%, 10%, 20% in successive years. What is the final amount?

Compound versus simple

Difference, relation and multiple-time

The difference of the two interests, getting one from the other, and the “how many times and when” questions.

The CI–SI difference

Interest on interest = the gap

In one year CI = SI; the 2- and 3-year difference formulas.

∑ Formula

C I - S I = P (\frac{R}{100})^{2} (2 वर्ष), C I - S I = P (\frac{R}{100})^{2} (3 + \frac{R}{100}) (3 वर्ष)

Difference formulas

Why? In the first year CI and SI are equal. In the second year CI also pays interest on the first year’s interest: $\frac{PR}{100} \times \frac{R}{100}$ — that is the gap. Also the 2-year $C I = S I (1 + \frac{R}{200})$ : given the SI you get CI directly.

Example 6 · Standard

Find the difference between CI and SI on ₹10,000 at 8% per annum for 2 years.

Solution, step by step

1Difference $= 10000 \times (\frac{8}{100})^{2}$ .
2 $= 10000 \times 0.0064 = 64$

Answer ₹64

Example 7 · Standard

The simple interest on a sum for 2 years at 10% is ₹1,200. What is the compound interest?

Solution, step by step

1 $C I = S I (1 + \frac{R}{200}) = 1200 \times 1.05$ .
2 $= 1260$

Answer ₹1,260

Example 8 · Advanced

The difference between CI and SI for 3 years at 20% per annum is ₹1,120. What is the principal?

Solution, step by step

1Difference $= P (0.2)^{2} (3 + 0.2) = P \times 0.04 \times 3.2 = 0.128 P$ .
2 $P = \frac{1120}{0.128} = 8750$

Answer ₹8,750

BasicTry it yourself first

What is the difference between the compound and simple interest on ₹5,000 at 10% per annum for 2 years?

StandardTry it yourself first

What is the difference between the compound and simple interest on ₹8,000 at 5% per annum for 2 years?

StandardTry it yourself first

What is the difference between the compound and simple interest on ₹12,500 at 4% per annum for 2 years?

AdvancedTry it yourself first

What is the difference between the compound and simple interest on ₹5,000 at 10% per annum for 3 years?

AdvancedTry it yourself first

What is the difference between the compound and simple interest on ₹6,250 at 20% per annum for 3 years?

BasicTry it yourself first

The difference between compound and simple interest for 2 years at 5% per annum is ₹10. What is the principal?

StandardTry it yourself first

The difference between compound and simple interest for 2 years at 8% per annum is ₹40. What is the principal?

AdvancedTry it yourself first

The difference between compound and simple interest for 2 years at 10% per annum is ₹150. What is the principal?

BasicTry it yourself first

The simple interest on a sum for 2 years at 10% per annum is ₹1,000. What is the compound interest on it for 2 years at the same rate?

StandardTry it yourself first

The simple interest on a sum for 2 years at 5% per annum is ₹800. What is the compound interest on it for 2 years at the same rate?

AdvancedTry it yourself first

The simple interest on a sum for 2 years at 8% per annum is ₹2,000. What is the compound interest on it for 2 years at the same rate?

How many times, and when

One multiplication, repeated

If a sum becomes $x$ times in $T$ years then in $k T$ years it becomes $x^{k}$ times.

In compound interest the sum is multiplied by the same ratio every $T$ years. Doubling in 5 years means it doubles again in the next 5 — 4 times in 10 years, 8 times in 15, 16 times in 20. This is unlike simple interest, where adding the doubling time again only makes it triple.

Example 9 · Standard

At compound interest a sum doubles in 4 years. In how many years will it become 8 times?

Solution, step by step

1 $8 = 2^{3}$ — doubling 3 times.
2Time $= 3 \times 4 = 12$ years

Answer 12 years

BasicTry it yourself first

At compound interest a sum becomes 2 times in 5 years. In how many years will it become 8 times?

StandardTry it yourself first

At compound interest a sum becomes 3 times in 3 years. In how many years will it become 9 times?

StandardTry it yourself first

At compound interest a sum becomes 2 times in 6 years. In how many years will it become 16 times?

AdvancedTry it yourself first

At compound interest a sum becomes 3 times in 8 years. In how many years will it become 27 times?

StandardTry it yourself first

At compound interest a sum amounts to ₹4,840 in 2 years and ₹5,324 in 3 years. What is the rate per annum?

AdvancedTry it yourself first

At compound interest a sum amounts to ₹8,820 in 2 years and ₹9,261 in 3 years. What is the rate per annum?

Instalments, population and depreciation

The same multiplier, a new story

Repaying a debt in equal annual instalments, and population or value rising and falling.

Equal annual instalments

The present value of each instalment

The loan = each instalment divided by the factor’s power for its year, added up.

∑ Formula

P = \frac{x}{1 + \frac{R}{100}} + \frac{x}{( 1 + \frac{R}{100} ) ^{2}} + \dots + \frac{x}{( 1 + \frac{R}{100} ) ^{n}}

The loan repaid by

n

equal annual instalments

Reason: the first instalment is paid one year later, so today it is worth $\frac{x}{1 + r}$ ; the second two years later, worth $\frac{x}{( 1 + r ) ^{2}}$ ; and so on. (Numbers are chosen for convenience: with $r = 10%$ and $x = 1331 m$ , three instalments repay a loan of $3310 m$ .)

Example 10 · Standard

A loan at 15% compound interest is repaid in 2 equal annual instalments of ₹1,058 each. How much was the loan?

Solution, step by step

1 $\frac{1058}{1.15} + \frac{1058}{1.3225} = 920 + 800$ .
2Loan $= 1720$

Answer ₹1,720

BasicTry it yourself first

A man borrowed on compound interest (10% per annum) and repaid in 2 equal annual instalments of ₹1,210 each. How much was the loan?

StandardTry it yourself first

A man borrowed on compound interest (5% per annum) and repaid in 2 equal annual instalments of ₹2,205 each. How much was the loan?

StandardTry it yourself first

A man borrowed on compound interest (10% per annum) and repaid in 3 equal annual instalments of ₹1,331 each. How much was the loan?

AdvancedTry it yourself first

A man borrowed on compound interest (25% per annum) and repaid in 3 equal annual instalments of ₹1,000 each. How much was the loan?

AdvancedTry it yourself first

A man borrowed on compound interest (20% per annum) and repaid in 2 equal annual instalments of ₹1,440 each. How much was the loan?

AdvancedTry it yourself first

A man borrowed on compound interest (10% per annum) and repaid in 3 equal annual instalments of ₹2,662 each. How much was the loan?

Population and depreciation

The same compound formula

Growing and shrinking quantities — a minus sign for a fall.

∑ Formula

बाद का मान = P (1 \pm \frac{R}{100})^{n}

+

for growth,

-

for decay

Population, price, a machine’s value (depreciation), number of trees, bacteria — all follow this formula.
For an earlier value divide: $earlier = \frac{now}{( 1 + r ) ^{n}}$ .
Different rates in different years (+10%, −20%, +30%): factors $1.1 \times 0.8 \times 1.3$ .

Example 11 · Standard

A town has a population of 80,000 growing 5% a year. What will it be after 2 years?

Solution, step by step

1 $80000 \times 1.0 5^{2} = 80000 \times 1.1025$ .
2 $= 88200$

Answer 88,200

Example 12 · Standard

An area has 6,000 people. It rises 10% in year 1, falls 20% in year 2 and rises 25% in year 3. How many at the end?

Solution, step by step

1Factor $1.1 \times 0.8 \times 1.25 = 1.1$ .
2 $6000 \times 1.1 = 6600$

Answer 6,600

BasicTry it yourself first

The population of a town is 50,000. Over 2 years it changes by +10%, +10% in turn. What will the population be at the end?

StandardTry it yourself first

The population of a town is 1,60,000. Over 3 years it changes by +5%, +5%, +5% in turn. What will the population be at the end?

StandardTry it yourself first

The value of a machine is 4,00,000. Over 3 years it changes by −10%, −10%, −10% in turn. What will the value be at the end?

StandardTry it yourself first

The population of a town is 20,000. Over 3 years it changes by +20%, −10%, +25% in turn. What will the population be at the end?

AdvancedTry it yourself first

The value of a machine is 6,40,000. Over 2 years it changes by −12.5%, −12.5% in turn. What will the value be at the end?

AdvancedTry it yourself first

The population of a town is 80,000. Over 4 years it changes by +25%, −20%, +10%, −10% in turn. What will the population be at the end?

BasicTry it yourself first

A town’s population rises 10% every year. It is 12,100 today. What was it 2 years ago?

StandardTry it yourself first

A town’s population rises 5% every year. It is 37,044 today. What was it 3 years ago?

AdvancedTry it yourself first

A town’s population rises 20% every year. It is 69,120 today. What was it 3 years ago?

Traps and fast tricks

Slips · tricks

Where marks go in compound interest.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Reading the answer as interest.

P (1 + r)^{n}

is the amount; subtract

P

for the CI.

Trap 2Changing only the rate or only the periods for half-yearly. Halve the rate and double the periods — both.

Trap 3Compounding the fractional year. Compound whole years; simple interest for the leftover months.

Trap 4Applying the CI–SI formula to one year. In one year they are equal — the gap is zero.

Trap 5Using $+$ for decay. The factor for a fall is

1 - \frac{R}{100}

Trap 6Treating the instalments’ total as the loan. They come later — divide each to get today’s worth.

Fast tricks

Remembered factors, difference formulas

Habits that shorten the work.

Know the factor table: 10% ⟹ 1.1, 1.21, 1.331; 20% ⟹ 1.2, 1.44, 1.728; 5% ⟹ 1.05, 1.1025.
2-year CI–SI: $P (\frac{R}{100})^{2}$ ; 3 years: $P (\frac{R}{100})^{2} (3 + \frac{R}{100})$ .
Think on 100: 10% for 2 years: 100 → 110 → 121; interest 21.
Rule of 72: the time to double is about $\frac{72}{R}$ years. At 12% that is about 6 years.
With two amounts given, their ratio is the factor: $\frac{A _{3}}{A _{2}} = 1 + \frac{R}{100}$ .

Example 13 · Standard

By the rule of 72, estimate the time for a sum to double at 9% compound interest per annum.

Solution, step by step

1Time $\approx \frac{72}{9}$ .
2 $= 8$ years (the real value ≈ 8.04)

Answer About 8 years

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

What is the amount on ₹6,000 after 2 years at 10% compound interest per annum?

BasicTry it yourself first

What is the amount on ₹2,000 after 2 years at 5% compound interest per annum?

BasicTry it yourself first

What is the compound interest on ₹3,000 at 10% per annum for 2 years, compounded annually?

BasicTry it yourself first

What is the compound interest on ₹10,000 at 5% per annum for 2 years, compounded annually?

BasicTry it yourself first

A sum amounts to ₹4,410 in 2 years at 5% compound interest per annum. What was the sum?

BasicTry it yourself first

A sum amounts to ₹7,260 in 2 years at 10% compound interest per annum. What was the sum?

BasicTry it yourself first

₹5,000 becomes ₹5,408 in 2 years at compound interest. What is the rate per annum?

BasicTry it yourself first

₹2,000 becomes ₹2,420 in 2 years at compound interest. What is the rate per annum?

BasicTry it yourself first

In how many years will ₹4,000 become ₹4,840 at 10% compound interest per annum?

BasicTry it yourself first

What is the half-yearly compound interest on ₹5,000 at 20% per annum for 1 year?

BasicTry it yourself first

₹2,000 is invested at compound interest with rates of 10%, 20% in successive years. What is the final amount?

BasicTry it yourself first

What is the difference between the compound and simple interest on ₹10,000 at 5% per annum for 2 years?

BasicTry it yourself first

The difference between compound and simple interest for 2 years at 5% per annum is ₹20. What is the principal?

BasicTry it yourself first

The simple interest on a sum for 2 years at 10% per annum is ₹800. What is the compound interest on it for 2 years at the same rate?

BasicTry it yourself first

At compound interest a sum becomes 2 times in 4 years. In how many years will it become 4 times?

BasicTry it yourself first

A man borrowed on compound interest (10% per annum) and repaid in 2 equal annual instalments of ₹1,210 each. How much was the loan?

BasicTry it yourself first

The population of a town is 1,00,000. Over 2 years it changes by +10%, +10% in turn. What will the population be at the end?

BasicTry it yourself first

A town’s population rises 10% every year. It is 24,200 today. What was it 2 years ago?

BasicTry it yourself first

At compound interest a sum amounts to ₹2,420 in 2 years and ₹2,662 in 3 years. What is the rate per annum?

BasicTry it yourself first

What is the interest on ₹4,000 at 10% per annum compounded annually for 1 years 6 months? (Simple interest on the part year.)

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

What is the amount on ₹20,000 after 3 years at 5% compound interest per annum?

StandardTry it yourself first

What is the amount on ₹16,000 after 2 years at 12.5% compound interest per annum?

StandardTry it yourself first

What is the compound interest on ₹32,000 at 5% per annum for 2 years, compounded annually?

StandardTry it yourself first

What is the compound interest on ₹7,500 at 20% per annum for 3 years, compounded annually?

StandardTry it yourself first

What is the compound interest on ₹6,250 at 8% per annum for 2 years, compounded annually?

StandardTry it yourself first

A sum amounts to ₹21,296 in 3 years at 10% compound interest per annum. What was the sum?

StandardTry it yourself first

A sum amounts to ₹13,891.5 in 3 years at 5% compound interest per annum. What was the sum?

StandardTry it yourself first

₹2,500 becomes ₹2,704 in 2 years at compound interest. What is the rate per annum?

StandardTry it yourself first

₹4,000 becomes ₹6,912 in 3 years at compound interest. What is the rate per annum?

StandardTry it yourself first

In how many years will ₹8,000 become ₹9,261 at 5% compound interest per annum?

StandardTry it yourself first

What is the half-yearly compound interest on ₹12,000 at 10% per annum for 1 year?

StandardTry it yourself first

What is the quarterly compound interest on ₹40,000 at 16% per annum for 0.5 years?

StandardTry it yourself first

What is the interest on ₹8,000 at 10% per annum compounded annually for 2 years 6 months? (Simple interest on the part year.)

StandardTry it yourself first

What is the interest on ₹12,500 at 8% per annum compounded annually for 1 years 9 months? (Simple interest on the part year.)

StandardTry it yourself first

₹7,500 is invested at compound interest with rates of 8%, 12.5%, 4% in successive years. What is the final amount?

StandardTry it yourself first

₹20,000 is invested at compound interest with rates of 10%, 5% in successive years. What is the final amount?

StandardTry it yourself first

What is the difference between the compound and simple interest on ₹25,000 at 6% per annum for 2 years?

StandardTry it yourself first

What is the difference between the compound and simple interest on ₹10,000 at 15% per annum for 3 years?

StandardTry it yourself first

The difference between compound and simple interest for 2 years at 4% per annum is ₹20. What is the principal?

StandardTry it yourself first

The difference between compound and simple interest for 2 years at 5% per annum is ₹50. What is the principal?

StandardTry it yourself first

The simple interest on a sum for 2 years at 8% per annum is ₹1,200. What is the compound interest on it for 2 years at the same rate?

StandardTry it yourself first

At compound interest a sum becomes 2 times in 4 years. In how many years will it become 8 times?

StandardTry it yourself first

At compound interest a sum becomes 3 times in 6 years. In how many years will it become 9 times?

StandardTry it yourself first

At compound interest a sum amounts to ₹7,290 in 2 years and ₹7,873.2 in 3 years. What is the rate per annum?

StandardTry it yourself first

A man borrowed on compound interest (5% per annum) and repaid in 2 equal annual instalments of ₹2,205 each. How much was the loan?

StandardTry it yourself first

A man borrowed on compound interest (10% per annum) and repaid in 3 equal annual instalments of ₹1,331 each. How much was the loan?

StandardTry it yourself first

The population of a town is 2,50,000. Over 2 years it changes by +8%, +8% in turn. What will the population be at the end?

StandardTry it yourself first

The value of a machine is 1,60,000. Over 3 years it changes by −10%, −10%, +25% in turn. What will the value be at the end?

StandardTry it yourself first

A town’s population rises 5% every year. It is 19,448.1 today. What was it 2 years ago?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

What is the amount on ₹64,000 after 3 years at 12.5% compound interest per annum?

AdvancedTry it yourself first

What is the compound interest on ₹1,28,000 at 25% per annum for 3 years, compounded annually?

AdvancedTry it yourself first

A sum amounts to ₹62,500 in 3 years at 25% compound interest per annum. What was the sum?

AdvancedTry it yourself first

A sum amounts to ₹20,250 in 2 years at 12.5% compound interest per annum. What was the sum?

AdvancedTry it yourself first

₹16,000 becomes ₹31,250 in 3 years at compound interest. What is the rate per annum?

AdvancedTry it yourself first

In how many years will ₹3,125 become ₹5,400 at 20% compound interest per annum?

AdvancedTry it yourself first

What is the half-yearly compound interest on ₹80,000 at 20% per annum for 1.5 years?

AdvancedTry it yourself first

What is the quarterly compound interest on ₹64,000 at 20% per annum for 1 year?

AdvancedTry it yourself first

What is the interest on ₹20,000 at 15% per annum compounded annually for 2 years 8 months? (Simple interest on the part year.)

AdvancedTry it yourself first

₹25,000 is invested at compound interest with rates of 4%, 6%, 8% in successive years. What is the final amount?

AdvancedTry it yourself first

₹40,000 is invested at compound interest with rates of 12.5%, 25%, 20% in successive years. What is the final amount?

AdvancedTry it yourself first

What is the difference between the compound and simple interest on ₹12,500 at 8% per annum for 3 years?

AdvancedTry it yourself first

What is the difference between the compound and simple interest on ₹80,000 at 5% per annum for 3 years?

AdvancedTry it yourself first

The difference between compound and simple interest for 2 years at 5% per annum is ₹80. What is the principal?

AdvancedTry it yourself first

The difference between compound and simple interest for 2 years at 10% per annum is ₹480. What is the principal?

AdvancedTry it yourself first

The simple interest on a sum for 2 years at 15% per annum is ₹7,200. What is the compound interest on it for 2 years at the same rate?

AdvancedTry it yourself first

At compound interest a sum becomes 2 times in 5 years. In how many years will it become 32 times?

AdvancedTry it yourself first

At compound interest a sum becomes 3 times in 7 years. In how many years will it become 27 times?

AdvancedTry it yourself first

At compound interest a sum amounts to ₹15,680 in 2 years and ₹17,561.6 in 3 years. What is the rate per annum?

AdvancedTry it yourself first

A man borrowed on compound interest (20% per annum) and repaid in 3 equal annual instalments of ₹1,728 each. How much was the loan?

AdvancedTry it yourself first

A man borrowed on compound interest (25% per annum) and repaid in 3 equal annual instalments of ₹1,250 each. How much was the loan?

AdvancedTry it yourself first

The value of a machine is 3,20,000. Over 3 years it changes by −5%, −5%, +10% in turn. What will the value be at the end?

AdvancedTry it yourself first

The population of a town is 4,50,000. Over 4 years it changes by +10%, −10%, +20%, −20% in turn. What will the population be at the end?

AdvancedTry it yourself first

A town’s population rises 12% every year. It is 78,400 today. What was it 2 years ago?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.