Question

Matt’s parents have agreed to contribute toward the rent for his apartment in his junior year in college. The plan is for Matt’s parents to deposit a lump sum in Matt’s bank account on August 1st and then have Matt withdraw $250 on the first of each month starting on September 1st and ending on May 1st the following year. If the bank pays interest on the balance at the rate of 5% per year compounded monthly, how much should Matt’s parents deposit into his account?

Answer 1

To find out how much Matt's parents should deposit into his account, we need to calculate the future value of the monthly withdrawals. Using the compound interest formula, we can determine that they should deposit around $2123.65 to cover the withdrawals and earn interest at a rate of 5% per year compounded monthly.

Step-by-step explanation:

To calculate how much Matt's parents should deposit into his account, we need to find the future value of the monthly withdrawals at the given interest rate. The formula for compound interest is:

FV = P(1 + r/n)^(nt)

Where FV is the future value, P is the principal (the amount deposited), r is the interest rate per period (5% in this case), n is the number of times interest is compounded per year (12 for monthly compounding), and t is the number of years. In this case, t is 9 months (September to May), so let's substitute the values into the formula:

FV = P(1 + 0.05/12)^(12 * 9)

FV = P(1.00416)^108

We want the future value to be $250 * 9 = $2250, so we can set up the equation:

$2250 = P(1.00416)^108

We can solve for P using algebra, which gives us:

P = $2250 / (1.00416)^108

Calculating this using a calculator or spreadsheet, we find that Matt's parents should deposit approximately $2123.65 into his account.