Question

person is planning to open a savings account with the intent to buy a house in 8 years. they will invest an equal amount each month for 8 years. the account will earn 9% annually and will have $450000 at the end of the 8 years. What amount is the monthly investment.

Answer 1

`\$3217.59`

Explanation:

We need to use the following formula:

`FV=P[ ((1+i)^(t) -1)/(r)]`

where

`FV` is the future value

`P` is the periodic payment

`r` is the monthly interest rate in decimal form

`t` is the number of months

In this problem we have

`FV=\$450,000`

`t=8\ years=96\ months`

`r=9\%/12=0.75\%=0.75/100=0.0075`

substitute in the equation above

`450,000=P[ ((1+0.0075)^(96) -1)/(0.0075)]`

solve for P

`450,000=P[ ((1.0075)^(96) -1)/(0.0075)]`

`P=450,000/[ ((1.0075)^(96) -1)/(0.0075)]`

`P=\$3217.59`