Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. (Use the tables in the handbook.)The best deal is:
A)Four Rivers
B)Four Rivers for first two years
C)Mystic
D)Mystic for last two years
E)None of these

Question

Quizplus · Accepted Answer

To determine the best deal, we calculate the future value of Jane's investment in both banks using the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.For Mystic Bank: $P = \$40,000$, $r = 12\% = 0.12$, $n = 4$ (since interest is compounded quarterly), and $t = 5$ years.$$A_{Mystic} = 40000(1 + \frac{0.12}{4})^{4*5}$$For Four Rivers Bank: $P = \$40,000$, $r = 14\% = 0.14$, $n = 2$ (since interest is compounded semiannually), and $t = 5$ years.$$A_{FourRivers} = 40000(1 + \frac{0.14}{2})^{2*5}$$Without calculating the exact amounts, the general principle is that a higher interest rate compounded less frequently can still yield a higher return than a lower interest rate compounded more frequently over the same period. Given the higher interest rate at Four Rivers (14% compounded semiannually) compared to Mystic (12% compounded quarterly), Four Rivers offers a better deal over the five-year period, assuming the difference in compounding frequency does not offset the higher rate advantage.

Jane Is Having Difficulty Deciding Whether to Put Her Savings