Compound Interest Quiz Set 011

Amount A = 8000000 × $(1 + 3/100)^3$, which equals 8000000 × $103/100$ × $103/100$ × $103/100$ = 8 × 103 × 103 × 103 = Rs. 8741816. So interest = A - P = 8741816 - 8000000 = Rs. 741816.

In this case r = $28/4$% and n = 3 because compounding is quarterly, and in 9 months there are three quarters. So A = 2000000 × $(1 + 7/100)^3$, which equals 2 × 107 × 107 × 107, i.e., Rs. 2450086.

The amount is 90000 + 9225. So 99225 = 90000 × $(105/100)^n$. So $99225/90000$ = $(105/100)^n$, which can be put in the form $(105/100)^2$ = $(105/100)^n$, so n = 2 years.

The amount is 8000000 + 741816. So 8741816 = 8000000 × $(103/100)^n$. So $8741816/8000000$ = $(103/100)^n$, which can be put in the form $(103/100)^3$ = $(103/100)^3$, so n = 3 years.

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × $((1 + r/100)^2 + (1 + r/100))$ = $P/10000$ × $((100 + r)^2 + 100(100 + r))$ = $P/10000 × (100 + r)$ × $(100 + r + 100)$ which equals ${P × (100 + r) × (200 + r)}/10000.$ Putting r = 5 and P = 50000 and cancelling 10000, we get 5 × 105 × 205 = Rs. 107625.