Suppose that your bank pays 10% interest, compounded semiannually. Use Table 12-2 of your text to find how much should be deposited now to yield an annuity payment of $400 at the END of every six months, for 4 years.
A) $2,585.28
B) $3,819.64
C) $1,267.95
D) $1,856.40

Question

Quizplus · Accepted Answer

The future value of an annuity is given by the formula:FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)where:PMT is the annuity paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:PMT = $400r = 10% = 0.10n = 2 (since the interest is compounded semiannually)t = 4Plugging these values into the formula, we get:FV = $400 * [(1 + 0.10/2)^(2*4) - 1] / (0.10/2)= $400 * [(1.05)^8 - 1] / 0.05= $400 * [1.480244 - 1] / 0.05= $400 * 0.480244 / 0.05= $3,841.95Therefore, the amount that should be deposited now to yield an annuity payment of $400 at the END of every six months, for 4 years, is $3,841.95.

Suppose That Your Bank Pays 10% Interest, Compounded Semiannually