Question

Find the monthly payment that will yield the future value of $95,000 using an ordinary annuity at 10% interest for 27 years. (Round the answer to the nearest cent

Answer 1

$57.73

Explanation:

We'll use the below formula to solve the given question;

`FV_{\text{ ordinary anuity}}=PMT((1+i)^n-1)/(i)`

where;

`\begin{gathered} FV=\text{ future value = \$95,000} \\ i=\text{interest rate =10/100 = 0.1 = 0.1/12 = 0.0083} \\ n\text{ = number of payments = 12 x 27= 324} \\ \text{PMT = monthly payment = ?} \end{gathered}`

Let's go ahead and substitute the above values into our formula and solve for PMT;

`\begin{gathered} 95000=PMT((1+(0.1)/(12))^(324)-1)/((0.1)/(12)) \\ 95000=PMT(13.714)/(0.0083) \\ 95000=1645.7024\text{PMT} \end{gathered}`

Let's divide both sides of the equation by 1645.7024;

`\begin{gathered} \text{PMT}=(95000)/(1645.7024) \\ \text{PMT}=\text{ \$}57.73 \end{gathered}`