Question

You plan to buy the house of your dreams in 17 years. You have estimated that the price of the house will be $88,158 at taht time. You are able to make equal deposits every month into a savings account at an annual rate of 3.33 percent, compounded monthly. How much money should you place in this savings account every month in order to accumulate the required amount to buy the house of your dreams? Round the answer to two decimal places.

Answer 1

Future Value of an Ordinary Annuity (Annuity Regular)

This is the case pf Future Value of an Ordinary Annuity and the monthly amount that should be placed each month is calculated as follows

Future Value = $88,158

Monthly Interest Rate (r) = 0.2775% per month [3.33% / 12 Months]

Number of months = 204 Months [17 Years x 12 Months]

Monthly Payment (P) = ?

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

$88,158 = P x [{(1 + 0.002775)²⁰⁴ – 1} / 0.002775]

$88,158 = P x [(1.76000 – 1) / 0.002775]

$88,158 = P x [0.76000 / 0.002775]

$88,158 = P x 273.87525

P = $88,158 / 273.87525

P = $321.89 per month

“Therefore, the amount of money that should be placed in the savings account every month in order to accumulate the required amount to buy the house = $321.89 per month”