A small foundry agrees to pay $250,000 two years from now to a supplier for a given amount of coking 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?
A)$29,770
B)$29,777
C)$29,740
D)$31,250

Question

Quizplus · Accepted Answer

To find the amount that must be deposited every three months, we can use the formula for the future value of an annuity:FV = PMT * (((1 + r/n)^(n*t)) - 1) / (r/n))where:FV is the future value of the annuityPMT is the payment amountr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $250,000r = 5.5% = 0.055n = 12 (since the interest is compounded monthly)t = 2Substituting these values into the formula, we get:$250,000 = PMT * (((1 + 0.055/12)^(12*2)) - 1) / (0.055/12))Solving for PMT, we get:PMT = $29,770Therefore, the foundry must deposit $29,770 every three months to have $250,000 in the account at the end of two years.

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