Question

Chris needs to buy a new stove in 5 years. He starts to deposit money quarterly, with the first saving in 3 month. If his investment earns 5% APR compounded semi-annually, how much he should invest every three month to buy a $2000 stove in 5 years? (Round your answer to two decimals.)

Answer 1

Semi annual rate = 5%/ 2 = 2.5%

(1 + semi annual rate)^n - 1 = (1 + quarterly rate)^4 - 1

(1 + 0.025)^2 - 1 = (1 + quarterly rate)^4 - 1

0.0506 = (1 + quarterly rate)^4 - 1

1.012417 = 1 + quarterly rate

Quarterly rate = 0.012417 or 1.2417%

Number of periods = 5 * 4 = 20

Future value = Payments * [(1 + r)^n - 1] / r

2000 = Payments * [(1 + 0.012417)^20 - 1] / 0.012417

2000 = Payments * [1.279937 - 1] / 0.012417

2000 = Payments * 22.544653

Payments = $88.71

He should invest $88.71