Question

Shelly’s investment of $3000 has been losing value at a rate of 3% each year. What will her investment be worth in 6 years?

Short answer

Shelly investment will be worth $2498.92 after 6 years.

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. 

Shelly invested $3000 for 6 years into an account with a $-3\%$interest rate compounded annually.

Substitute 3000 for P, $-3$for r, 1 for n and 6 for t into the formula$A=P{\left(1+\frac{r}{n}\right)}^{nt}$.

$$\begin{gathered} \text{A}=P{\left(1+\frac{r}{n}\right)}^{n·t} \\ =3000\times {\left(1-\frac{0.03}{1}\right)}^{1\times 6} \end{gathered}$$

Step 3. Simplify for A.

Simplify the equation for A.

$$\begin{gathered} \text{A}=P{\left(1+\frac{r}{n}\right)}^{n·t} \\ =3000\times {\left(1-\frac{0.03}{1}\right)}^{1\times 6} \\ =3000\times {\left(0.97\right)}^6 \\ =\$2498.92 \end{gathered}$$

Thus, Shelly investment will be worth $2498.92 after 6 years.