A small foundry agrees to pay $250,000 two years from now to a supplier for a given amount ofcoking coal. The foundry plans to deposit a fixed amount in a bank account every three months, starting three months from now, so that at the end of two years the account holds $250,000. If the account pays 5.5% APR compounded monthly, how much must be deposited every three months?

Question

Quizplus · Accepted Answer

Using the formula for future value of an annuity: 
FV = PMT * [(1 + i)^n - 1]/i
where PMT is the quarterly deposit, i is the monthly interest rate (0.055/12), and n is the total number of periods (2 years * 4 quarters/year = 8 quarters).

We want the FV to be $250,000, so: 
$250,000 = PMT * [(1 + 0.055/12)^8 - 1]/(0.055/12)
Solving for PMT gives: 
PMT = $29,769.67

Rounding up to the nearest dollar gives the answer of $29,770, which is choice (B).

A Small Foundry Agrees to Pay $250,000 Two Years from Now