Loren wants to invest $\$ 6,500$ in a fund at an interest rate of $7.5 \%$ Per year, compounded monthly. How long will it take her investment to grow to $\$ 7,850 ?$
A) $2.5 \text { years }$
B) $25 \text { years }$
C) $0.5 \text { years }$
D) $4.5 \text { years }$
E) $1 \text { year }$

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to grow to a certain amount with compound interest, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ 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. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{n \log(1 + r/n)}$. Plugging in the values: $A = 7850$, $P = 6500$, $r = 0.075$, and $n = 12$, we find that $t$ is approximately $2.5$ years.

Loren Wants to Invest $6,500\$ 6,500$6,500 In a Fund at an Interest Rate Of

Loren Wants to Invest $\$ 6,500$ In a Fund at an Interest Rate Of