#### Question

Kamala borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?

(Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2^{nd} year amount for `4/12` years.)

#### Solution

Principal (P) = Rs 26,400

Rate (R) = 15% per annum

Number of years (*n*) = `2 4/12` year

The amount for 2 years and 4 months can be calculated by first calculating the amount for 2 years using the compound interest formula, and then calculating the simple interest for 4 months on the amount obtained at the end of 2 years.

Firstly, the amount for 2 years has to be calculated.

`A = Rs [26400(1 + 15/100)^2] = Rs [26400 (1 + 3/20)^2]`

= `Rs (26400 xx23/20 xx23/20)` = Rs 34914

By taking Rs 34,914 as principal, the S.I. for the next `1/3` years will be calulated

S.I. Rs `((34914 xx 1/3 xx 15)/100)` = Rs . 1745.70

Interest for the first two years = Rs (34914 − 26400) = Rs 8,514

And interest for the next `1/3` year = Rs 1,745.70

Total C.I. = Rs (8514 + Rs 1745.70) = Rs 10,259.70

Amount = P + C.I. = Rs 26400 + Rs 10259.70 = Rs 36,659.70