Compound Interest Quiz Set 017

Amount A = 50000 × $(1 + 4/100)^2$, which equals 50000 × $104/100$ × $104/100$ = 5 × 104 × 104 = Rs. 54080. So interest = A - P = 54080 - 50000 = Rs. 4080.

The shortcut formula for the difference between compound and simple interest over a period of 2 years is $Difference = Principal × (\text"rate"/100)^2$. So Principal = $(Difference × 10000)/(rate × rate)$ = $(343 × 10000)/(7 × 7)$ = Rs. 70000.

Amount A = 20000 × $(1 + 5/100)^2$, which equals 20000 × $105/100$ × $105/100$ = 2 × 105 × 105 = Rs. 22050. So interest = A - P = 22050 - 20000 = Rs. 2050.

Amount A = 30000 × $(1 + 9/100)^2$, which equals 30000 × $109/100$ × $109/100$ = 3 × 109 × 109 = Rs. 35643. So interest = A - P = 35643 - 30000 = Rs. 5643.

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 = 2 and P = 10000 and cancelling 10000, we get 1 × 102 × 202 = Rs. 20604. Please note that the rate of interest will be 1/2 because the compounding is half yearly.