$$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$$
-Suppose that you have $3000 to invest. Which investment yields the greater return over 9 years: 5.4% compounded monthly or 5.5% compounded quarterly?
A)$3000 invested at 5.4% compounded monthly over 9 years yields the greater return.
B)Both investment plans yield the same return.
C)$3000 invested at 5.5% compounded quarterly over 9 years yields the greater return.

Question

Quizplus · Accepted Answer

To compare the two investments, we use the compound interest formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$ for each scenario. For the first investment at 5.4% compounded monthly, $P = 3000$, $r = 0.054$, $n = 12$, and $t = 9$. For the second investment at 5.5% compounded quarterly, $P = 3000$, $r = 0.055$, $n = 4$, and $t = 9$. Calculating each:1. $A_1 = 3000 \left(1 + \frac{0.054}{12}\right)^{12 \cdot 9}$2. $A_2 = 3000 \left(1 + \frac{0.055}{4}\right)^{4 \cdot 9}$Comparing the results, the investment at 5.5% compounded quarterly yields a greater return due to the higher interest rate and the effect of compounding, despite being compounded less frequently than the monthly option.

Use the compound interest formulas A=P(1+rn)nt and A=Pert to solve. \text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. } Use the compound interest formulas A=P(1+nr​)nt and A=Pert to solve.

$\text { Use the compound interest formulas } A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { and } A = P e ^ { r t } \text { to solve. }$