The simple interest on a sum of money for 2 years at 10% p.a. is ₹ 1,700. Find:

(i) the sum of money,

(ii) the compound interest on this sum for 1 year, payable half yearly at the same rate.

(i) Given,

The simple interest on a sum of money for 2 years at 10% p.a. is ₹ 1700.

I = ₹ 1,700

T = 2 year

R = 10%

Let sum of money be ₹ P.

I = $\dfrac{P \times R \times T}{100}$

Substituting values we get :

$\Rightarrow 1700 = \dfrac{P \times 10 \times 2}{100} \\[1em] \Rightarrow 1700 = \dfrac{P \times 20}{100}\\[1em] \Rightarrow 1700 = \dfrac{P}{5} \\[1em] \Rightarrow P = 1700 \times 5 = 8,500.$

Hence, the sum of money = ₹ 8,500

(ii) Given,

For first half year :

P = ₹ 8,500

R = 10%

Half yearly rate = $\dfrac{Rate}{2} = \dfrac{10}{2}$ = 5%

T = 1 half year

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{8500 \times 5 \times 1}{100} = ₹ 425$

Amount = P + I = ₹ 8,500 + ₹ 425 = ₹ 8,925.

For second half year :

P = ₹ 8,925

Half yearly rate = 5%

T = 1 half year

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{8925 \times 5 \times 1}{100} = ₹ 446.25$

Amount = P + I = ₹ 8,925 + ₹ 446.25 = ₹ 9,371.25

Compound interest = Final Amount - Initial Pincipal

= ₹ 9,371.25 - ₹ 8,500

= ₹ 871.25

Hence, compound interest = ₹ 871.25