Question

A principal of $5000 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 9 years? Round up your answer to the nearest dollar.

Answer 1

Given the following data:

Principal = $5000

Rate of interest = 8.5%

Time = 9 years

To find the total amount of money that the investor would have after 9 years:

Mathematically, compound interest is given by the formula:

`A=P(1+i)^t`

Where,

`\begin{gathered} A=Future\text{ value} \\ P=Pr\text{incipal or starting amount} \\ i=Annual\text{ inter}ets\text{ rate=}(r)/(100)=(8.5)/(100)=0.085 \\ t=nu\text{mber of years} \end{gathered}`

Substituting the given parameters into the formula, we have;

`\begin{gathered} A=5000(1+0.085)^9 \\ \therefore A=5000(1.085)^9=10419.27853 \\ \text{Hence,} \\ A=10419.27853 \end{gathered}`

Now, we can find the total amount of money that the investor would have after 9 years:

Total amount of money = Amount + Principal

Total amount of money = 10419.27583 + 5000 = 15419.27853

Therefore,

`15419.27853\approx15419\text{ (nearest dollar)}`

Hence, the total amount is $ 15,419.