Question

Nikita invests rs 6000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to rs 6720.
Calculate:
a) the rate of interest
b) the amount at the end of the second year.

Answer 1

Given:

Nikita invests a sum of money = Rs. 6000

Time period = 2 years

At the end of the first year the sum of money amounts to Rs. 6720

To find:

a) The rate of interest

b) The amount at the end of the second year.

Formula to find the amount in case of compound interest:

$\boxed{\bold{A\:=\:P[1\:+\:\frac{R}{100} ]^n}}$

where

A = amount

P = sum of money

R = rate of interest

n = time period

Solution:

(a). Finding the rate of interest:

Since the amount at the end of the first year is Rs. 6720, so we will calculate the rate of interest by substituting n = 1 year, A = Rs. 6720 and P = Rs. 6000  in the formula,

∴ $6720\:=\:6000[1\:+\:\frac{R}{100} ]^1$

⇒ $\frac{6720}{6000} = [1\:+\:\frac{R}{100} ]$

⇒ $1.12 = [1\:+\:\frac{R}{100} ]$

⇒ $1.12 - 1 = \:\frac{R}{100}$

⇒ $0.12 = \frac{R}{100}$

⇒ $\bold{R = 12\:\%}$

Thus, the rate of interest is 12%.

(b). Finding the amount at the end of the second year

Here to find the amount at the end of the 2nd year we will substitute P = Rs. 6000, n = 2 years & R = 12% in the formula, we get

∴ $A\:=\:6000[1\:+\:\frac{12}{100} ]^2$

⇒ $A = 6000\:\times\:[\frac{100+12}{100} ]^2$

⇒ $A = 6000\:\times\:[\frac{112}{100} ]^2$

⇒ $A = 6000\:\times\:[1.12 ]^2$

⇒ $A = 6000\:\times\:1.2544$

⇒ $\bold{A = Rs.\: 7526.40}$

Thus, the amount at the end of the second year is Rs. 7526.40.

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Answer 2

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