We were given the following information:
Age = 31
Deposit (Principal) = $90
Interest = 5% compounded monthly (12 times every year)
a. At age 60, the time that would have elapsed is: 60 - 31 = 29 years
The amount you will have in the IRA is calculated using the formula below:
[tex]\begin{gathered} A=\frac{P\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{\frac{r}{n}} \\ P=\text{\$}90 \\ r=5\text{\% }=0.05 \\ n=12 \\ t=29years \\ \text{We will go ahead and substitute the values of the variables into the equation, we have:} \\ A=\frac{90\lbrack(1+\frac{0.05}{12})^{12\times29}-1\rbrack}{\frac{0.05}{12}} \\ A=\frac{90\lbrack(4.2503-1)\rbrack}{0.00417} \\ A=\frac{90(3.2503)}{0.00417} \\ A=\frac{292.527}{0.00417}=70,150.36 \\ A=\text{\$}70,150.36 \\ \\ \therefore A=\text{\$}70,150.36 \end{gathered}[/tex]
Therefore, at age 61, you will have $70,150.36 in your IRA
b. The interest is given as shown below:
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