Melissa is saving for a car. She deposits a fixed amount every month in a bank account with an EAR of 5.5%. If this account pays interest every month then how much should she save from each monthly wage in order to have $15 000 in the account in three years' time?
A)$348
B)$396
C)$4 620
D)$385

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of an annuity, which is FV = P * [(1 + r)^n - 1] / r, where FV is the future value ($15,000), P is the monthly payment we need to find, r is the monthly interest rate (EAR of 5.5% divided by 12), and n is the total number of payments (3 years * 12 months = 36). The EAR of 5.5% needs to be converted to a monthly rate, which is 5.5% / 12 = 0.4583% or 0.004583 as a decimal. Plugging the values into the formula gives us $15,000 = P * [(1 + 0.004583)^36 - 1] / 0.004583. Solving for P gives us approximately $385.

Melissa Is Saving for a Car