Harrison has an account with the balance of $155.59 this account has an interest rate of 9.4 % compound annually and the initial investment was two years ago. How much was the initial investment?

Answer :

To answer this problem, we need to use the compound interest formula, which is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A represents the final amount, P represents the principal(initial investment), r represents the interest rate in decimals, n represents the number of times interest is compounded per unit t, and t the amount of time.

We have the final balance of Harrison's account, which is our value A

[tex]A=155.59[/tex]

The interest rate is 9.4%. To convert a percentage to a decimal, we just divide the percentage value by 100.

[tex]r=9.4\%=\frac{9.4}{100}=0.094[/tex]

The initial investment was two years ago, therefore, the time period is 2.

[tex]t=2[/tex]

And since the interest is compounded anually and the time period unit is year, we have

[tex]n=1[/tex]

Plugging all those values in the formula, we have

[tex]155.59=P(1+\frac{0.094}{1})^{1\cdot2}[/tex]

Solving for P, we have

[tex]\begin{gathered} 155.59=P(1+\frac{0.094}{1})^{1\times2} \\ 155.59=P(1.094)^2 \\ P=130.001102908... \\ P\approx130.00 \end{gathered}[/tex]

The initial investment was $130.00.