Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after years if the interest is

(i) Compounded annually

(ii) Compounded half yearly

(i) P = Rs 80,000

R = 10% per annum

n =years

The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.

Firstly, the amount for 1 year has to be calculated.

By taking Rs 88,000 as principal, the SI for the next year will be calculated.

Interest for the first year = Rs 88000 − Rs 80000 = Rs 8,000

And interest for the nextyear = Rs 4,400

Total C.I. = Rs 8000 + Rs 4,400 = Rs 1,2400

A = P + C.I. = Rs (80000 + 12400) = Rs 92,400

(ii) The interest is compounded half yearly.

Rate = 10% per annum = 5% per half year

There will be three half years inyears.

Difference between the amounts = Rs 92,610 − Rs 92,400 = Rs 210