Question

Howard is saving for a long holiday. He deposits a fixed amount every month in a bank account with an EAR of 10.8%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $13,000 in the account in four years' time? O A. $308 OB. $352 O C. $220 OD. $176

Answer 1

Let the amount saved each month be P

Monthly Interest Rate = r = 0.108/12

Number of months = n = 4*12 = 48 months

Future Value required = FV = $13000

Hence, FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r

=> 13000 = P[(1+0.108/12)⁴⁸ -1]/(0.108/12)

=> P = 13000*(0.108/12)/[(1+0.108/12)⁴⁸ -1] = $217.73

Hence, he should deposit $220 each month in the account