Question

HW13. Suppose that you begin saving up to buy a car by depositing a certain amount at the end of each month in a savings account which pays 3.6% annual interest compounded monthly. If your goal is to have $15,000 in the account four and a half years from now, how much do you need to put into the savings account each month

Answer 1

$256.31

Step-by-step explanation:

Interest rate per annum = 3.6%

Number of years = 4.5

No of payment per annum = 12

Interest rate per period 3.6%/12 = 0.3%

Number of period = 4.5*12 = 54

FV of annuity = 15,000

Deposit in each month (P) = FVA / ([1+r)^n - 1]/r)

Deposit in each month (P) = 15,000 / ([1+0.3%]^54 - 1) / 0.3%)

Deposit in each month (P) = 15,000 / ([1.003^54 - 1]/0.003)

Deposit in each month (P) = 15,000 / (1.175575 - 1/0.003)

Deposit in each month (P) = 15,000 / (0.175575/0.003)

Deposit in each month (P) = 15,000 / 58.525

Deposit in each month (P) = 256.3007262

Deposit in each month (P) = $256.31