A man borrowed ₹ 16000 for 3 years under the following terms :

20% simple interest for the first 2 years.

20% C.I. for the remaining one year on the amount due after 2 years, the interest being compounded half-yearly.

Find the total amount to be paid at the end of three years.

For S.I. :

P = ₹ 16000

Time = 2 years

Rate = 20%

S.I. = $\dfrac{P \times R \times T}{100} = \dfrac{16000 \times 2 \times 20}{100}$ = ₹ 6400.

Amount = P + S.I. = ₹ 16000 + ₹ 6400 = ₹ 22400.

For C.I. :

P = ₹ 22400

Time = 1 year

Rate = 20%

When interest is compounded half-yearly :

A = $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2}$

Substituting values we get :

$A = 22400\Big(1 + \dfrac{20}{2 \times 100}\Big)^{1 \times 2} \\[1em] = 22400 \times \Big(1 + \dfrac{1}{10}\Big)^2 \\[1em] = 22400 \times \Big(\dfrac{11}{10}\Big)^2 \\[1em] = 22400 \times \dfrac{121}{100} \\[1em] = 224 \times 121 \\[1em] = ₹ 27104.$

Hence, total amount to be paid = ₹ 27104.