Question

Lynne invested \(500 into an account with a 6.5% interest rate compounded monthly. How much will Lynne’s investment be worth in 10 years?

F \)600.00

G \(938.57

H \)956.09

J $957.02

Short answer

Lynne will get $956.09 after 10 years. Option H is correct choice.

Step-by-step solution

Step 1. Write the compound interest equation.

The compound interest equation is given by:

$A=P{\left(1+\frac{r}{n}\right)}^{nt}$, where A is the amount, P is the principal amount, r is the rate of interest, t is the time.

Step 2. Substitute the values. 

Lynne invested $500 for 10 years into an account with a 6.5 % interest rate compounded monthly.

Substitute 500 for P, 6.5 for r, 12 for n and 10 for t into the formula$A=P{\left(1+\frac{r}{n}\right)}^{nt}$.

$$\begin{gathered} \text{A}=P{\left(1+\frac{r}{n}\right)}^{n·t} \\ =500\times {\left(1+\frac{0.065}{12}\right)}^{12\times 10} \end{gathered}$$

Step 3. Simplify for A.

Simplify the equation for A.

$$\begin{gathered} \text{A}=P{\left(1+\frac{r}{n}\right)}^{n·t} \\ =500\times {\left(1+\frac{0.065}{12}\right)}^{12\times 10} \\ =500\times {\left(\frac{12.065}{12}\right)}^{120} \\ =\$956.09 \end{gathered}$$

Thus, Lynne will get $956.09 after 10 years. Option H is correct choice.