Question

Tommy wishes to retire at the age of 67 with $95,000 in savings. Determine the monthly payment into an IRA if the APR is 6.8% and he begins making payments at:Step 1: 25 years oldThe next part is finding the answer for 35 years old

Answer 1

Step 1

State the annuity formula

`A=(P[(1+(r)/(n))^(nt)-1])/((r)/(n))`

where;

`\begin{gathered} P=? \\ r=6.8\text{\%=}(6.8)/(100)=0.068 \\ n=12 \\ t=67-25=42 \\ A=\text{ \$95000} \end{gathered}`

Step 2

Find the monthly payment from 25 years old

`95000=(P[(1+(0.068)/(12))^(42*12)-1])/((0.068)/(12))`
`\begin{gathered} (0.068P\left[\left(1+(0.068)/(12)\right)^(42* \:12)-1\right])/((0.068)/(12))=95000* \:0.068 \\ 195.02614P=6460 \\ (195.02614P)/(195.02614)=(6460)/(195.02614) \\ P=33.1237639 \\ P\approx\text{ \$}33.12 \end{gathered}`

Step 3

Find the monthly payment from 35 years old

`\begin{gathered} 95000=(P[(1+(0.068)/(12))^(32*12)-1])/((0.068)/(12)) \\ n=67-35=32 \\ (P\left[\left(1+(0.068)/(12)\right)^(32* \:12)-1\right])/((0.068)/(12))=95000 \\ (0.068P\left[\left(1+(0.068)/(12)\right)^(32* \:12)-1\right])/((0.068)/(12))=95000* \:0.068 \\ 93.08447P=6460 \\ P=69.39933 \\ P=\text{\$69.40} \end{gathered}`

Answer;

`\text{ \$69.40}`