Question

Your investment account pays 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Answer 1

Answer:

8 years.

Explanation:

We have been given that an investment account pays 8.0%, compounded annually. We are asked to find the number of years it will take for the investment to grow to $9,140.20, if you invest $5,000 today.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$, where.

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

$8.0\%=\frac{8.0}{100}=0.08$

Upon substituting our given values in above formula, we will get:

$\ 9,140.20=\ 5,000(1+\frac{0.08}{1})^{1*t}$

$\ 9,140.20=\ 5,000(1+0.08)^{t}$

$\ 9,140.20=\ 5,000(1.08)^{t}$

$1.08^{t}=\frac{\ 9,140.20}{\ 5,000}$

$1.08^{t}=1.82804$

Now, we will take natural log of both sides.

$\text{ln}(1.08^{t})=\text{ln}(1.82804)$

Using log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$, we will get:

$t\cdot \text{ln}(1.08)=\text{ln}(1.82804)$

$t=\frac{\text{ln}(1.82804)}{\text{ln}(1.08)}$

$t=7.83830\approx 8$

Therefore, it will take approximately 8 years for the investment to grow to $9,140.20.