Question

Age 34 deposit $40 at the end of each month an IRA that pays 4.5% compounded interest monthly a how much will you have at age 65 be the interest is approximately

Answer 1

Given

`\begin{gathered} d=\text{ the regular deposit =40} \\ r=0.045\text{ \% \lparen4.5\%\rparen} \\ k=k=12\text{ }compounds/depositsperyear \\ t=65years-34years=31years \end{gathered}`

Step-by-step explanation

We can then use the annuity formula to find the amount the person will have at age 65.

`P_N=(d((1+(r)/(k))^(Nk)-1))/((r)/(k))`

Therefore, we will have;

`\begin{gathered} P_(31)=(40((1+0.045\/12)^(31*12)-1))/((0.045)/(12)) \\ =(40\left(\left((0.045)/(12)+1\right)^(372)-1\right))/((0.045)/(12)) \\ =(40\left(\left(1+(0.045)/(12)\right)^(372)-1\right)*\:12)/(0.045) \\ =(480\left(1.00375^(372)-1\right))/(0.045) \\ =(1451.74110)/(0.045) \end{gathered}`