Solve the problem. Round to the nearest cent as needed.
-Cara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How much should she invest now at 12%, compounded quarterly, so that she will have enough to buy a new car?
A) $10,520.70
B) $12.594.29
C) $11,957.91
D) $9532.77

Question

Quizplus · Accepted Answer

To find out how much Cara should invest now to have $15,000 in 3 years at a 12% annual interest rate compounded quarterly, we use the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the future value, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal), $n$ is the number of times the interest is compounded per year, and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $P$, we get $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Plugging in the values: $A = 15000$, $r = 0.12$, $n = 4$ (since interest is compounded quarterly), and $t = 3$, we find the initial investment required.

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