The principle of compounding growth is used extensively in the financial world to transform small savings into a big corpus over time. It’s also the underlying idea behind MBA topics such as *time value of money* and *discounted cash flow (DCF) valuation*.

Learn about simple and compound interest concepts as you’ll need them not only for entrance exams but in the real world too, especially after you become rich and famous.

Here is a list of some basic definition and formulas to solve problems on Interest.

**Principal**: This is the sum of money lent or borrowed.

**Interest**: This is the extra money paid for taking the money as loan. This is often expressed as a percentage.

Say, the interest is 10% on a loan of Rs. 100. Then the interest in amount is Rs. 10 and at the end of the year, the amount to be paid is Rs. 110.

**Time**: This is the time period for which the money is lent or the time period in which the money has to be returned with interest.

As the name implies, the calculation of simple interest is pretty simple. Multiply the principal amount with the number of years and the rate of interest.

*Simple Interest Formula:*

Simple Interest = Principal * Time * Rate of interest / 100

Abbreviated as SI = PTR/100

In compound interest, the principal amount with interest after the first unit of time becomes the principal for the next unit.

Say, when compounded annually for 2 years, the principal amount with interest accrued at the end of first year becomes the principal for the second year.

*Compound Interest Formula:*

Amount = Principal * [1 + Rate of Interest/100]^{Time period}

Abbreviated as Amount = P * [1 + R/100]^{t}, when compounded annually.

Sometimes, the interest is also calculated half-yearly or quarterly.

When compounded semi-annually or half-yearly,

Amount = P[1 + (R/2)/100]^{2t}

When compounded quarterly,

Amount = P[1 + (R/4)/100]^{4t}

Present worth of Principal P due t years hence is given by:

P/[1+ R/100]^{t}

Let us work on some examples to understand the concepts and the differences.

**Problem 1.** A sum of Rs. 25000 becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.

__Solution__:

Simple interest = 27250 – 25000 = 2250

Time = 3 years.

SI = PTR / 100 → R = SI * 100 / PT

R = 2250 * 100 / 25000 * 3 → R = 3%.

**Problem 2.** Find the present worth of Rs. 78000 due in 4 years at 5% interest per year.

__Solution__:

Amount with interest after 4 years = Rs. 78000

Therefore, simple interest = 78000 – Principal.

Let the principal amount be p.

78000 – p = p*4*5/100 → p=13000

Principal = 78000 – 13000 = Rs. 65000

**Problem 3.** A certain principal amounts to Rs. 15000 in 2.5 years and to Rs. 16500 in 4 years at the same rate of interest. Find the rate of interest.

__Solution__:

Amount becomes 15000 in 2.5 years and 16500 in 4 years.

Simple interest for (4-2.5) years = 16500 – 15000

Therefore, SI for 1.5 years = Rs. 1500.

SI for 2.5 years = 1500/1.5 * 2.5 = 2500

Principal amount = 15000 – 2500 = Rs. 12500.

Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%.

**Problem 4.** Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.

__Solution__:

Amount with CI = 3000 (1+ 5/100)^{2} = Rs. 3307.5

Therefore, CI = 3307.5 – 3000 = Rs. 307.5

**Problem 5.** Find the compound interest on Rs. 10000 at 12% rate of interest for 1 year, compounded half-yearly.

__Solution__:

Amount with CI = 10000 [1+ (12/2 * 100)]^{2 } = Rs. 11236

Therefore, CI = 11236 – 10000 = Rs. 1236

**Problem 6.** The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal.

__Solution__:

Let the principal amount be x.

SI = x * 2 * 8 / 100 = 4x/25

CI = x[1+ 8/100]^{2} – x → 104x/625

Therefore, 104x/625 – 4x/25 = 12.80

Solving which gives x, Principal = Rs. 2000.

**Problem 7.** Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.

__Solution__:

Let the rate of interest be r.

5000[1+ r/100]^{2} = 5000+253.125

→ [1+r/100]^{2} = 5253.125/5000

Solving which gives

[1+ r/100]^{2} = 1681/1600

→ 1+r/100 = 41/40

→ r = 2.5

Therefore, SI = 5000* 2 * 2.5/ 100 = Rs. 250.

**Problem 8.** A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?

__Solution__:

SI on Rs. 5760 for 1 year = 6912 – 5760 = Rs. 1152

Therefore, Rate of interest for 1 year = 100*1152/5760*1 = 20%

Let the principal be p.

Then, Principal = p[1+ 20/100]^{2 }= 5760

Solving which gives Principal = Rs. 4000

**Problem 9.** How long will it take a certain amount to increase by 30% at the rate of 15% simple interest?

__Solution__:

Let the principal be Rs. x

Simple interest = x*30/100 = 3x/10

T = 100*SI/PR = 100*3x/10 / x*15 = 2%

Alternatively, this can be solved by considering principal amount to be Rs. 100. Then simple interest becomes Rs. 30.

Then, T = 100*30/100*15 = 2%

Problem 1

A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.

A. 3.5

B. 3.75

C. 4

D. 4.5

Answer 1

A.

**Explanation**

(1000*t*3/100) + (1400*t*5/100) = 350 → t =3.5

Problem 2

Find the present worth of Rs. 20872.5 due 2 years hence at 10% rate of interest.

A. 17500

B. 17520

C. 17750

D. 17250

Answer 2

D.

**Explanation**:

Present worth = 20872.5/[1+ 10/100]^{2}

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## 12 Comments

tell me the procedure for this problems immediately sir

A certain sum when invested for 2 years at 20% per annum Compound Interest (compounded annually), earns Rs.2288 as interest. What will oe the interest earned if the same sum of money is invested for 5 years at 12 % per annum Simple Interest ?

The compound interest (compounded annually) on Rs. 9300/- Tor 2 years @ R% p.a. is Rs. 4092/-. Had the rate of interest been (R-10)%, what would have been the interest on the same sum of money for the same time (2 years) ?

Train A can completely cross train B (from the moment they meet), travelling in opposite direction (towards each other), in 14 seconds. If the speed of trains A and B are 65 kmph and 52 kmph respectively and the length of train A is 71 m more than that of train B, what is the length of train A ? (in m)

men can finish a project in 45 days. Only 36 men started working and after 4 days 12 women replaced them. If these 12 women could finish the remaining work in 54 days, how many days will only 12 women take to finish the complete project ?

Let the sum be x.

Then, CI amount = x(1+20/100)square= 2288.

=> x(1.2)square= 2288+x

=> 1.44x = 2288+x

=> 0.44x = 2288

=> x = 2288/0.44

=> x = 5200.

Now, principle is equal to 5200.

Thus, interest earned @ 12% p.a SI after 5 years will be = (5200*12*5)/100 = Rs. 3120.

I am not getting problem no 2 please help me out

P=1500 A=1900 r=? T=3

Ram invested total sum of 18000rs. In two schemes A &B for two years scheme A. Offers C.I @10 p.c.p.a , and scheme B offers. S.I @ 8 p.c.p.a. if the total interest earned by him from both schems after 2 years is 3510 rs . How much money (principal) did he invested in scheme B?

600 rs invested by compound interest

17400rs invested by simple interest

Could you please solve this problem sir….

Mr. X invested certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and the simple interest of 3 years and that of 2 years is 25:8 . The rate of interest per annum is ?

If the interest collected after 5th year is 51840 and after 6th year is 62208 compounded annually. Find the rate of interest?

THE DIFFERENCE BETWEEN THE COMPOUND INTEREST AND SIMPLE INTEREST FOR 3 YEARS AT 5% P.A. ON A CERTAIN SUM OF MONEYWAS Rs610 FIND THE SUM

Rashi invested RS.16000 for 2 years at Compound Interest and received an amount of RS.17640.What is the rate of interest?

Help me to solve this.

17640 =16000{1+r/100)^2

you get

11025 ={100+r)^2;

100+r =105;

r=5% is the answer

Kashis Deposited rs50000 @ 4% in saving account .

After 5 Years he withdrew rs 10000 and total interest of 5 Yrs how long should he keep the remaining amount to get total interest rs 14800 from the beginning .