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vivado [14]
3 years ago
11

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

ent to grow to $9,140.20?
Business
1 answer:
Rashid [163]3 years ago
8 0

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.

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