Question

At the age of 31, to save for retirement, you decide to deposit $90 at the end of each month in an IRA that pays 5% compounded monthly

Answer 1

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:

`\begin{gathered} A=(P\lbrack(1+(r)/(n))^(nt)-1\rbrack)/((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=(90\lbrack(1+(0.05)/(12))^(12*29)-1\rbrack)/((0.05)/(12)) \\ A=(90\lbrack(4.2503-1)\rbrack)/(0.00417) \\ A=(90(3.2503))/(0.00417) \\ A=(292.527)/(0.00417)=70,150.36 \\ A=\text{\$}70,150.36 \\ \\ \therefore A=\text{\$}70,150.36 \end{gathered}`

Therefore, at age 61, you will have $70,150.36 in your IRA

b. The interest is given as shown below: