Question

You currently have $2,500 in your savings account. You would like to have $10,000 five years from today. How much must you deposit in equal amounts at the end of each month for the next five years in order to reach your goal at an interest rate of 9% per year, compounded monthly?

Answer 1

Step 1 - Find out the future value of $2500 at the end of 5th year
Using Future value of sum formula , we can find out this value.
Future value = P x (1+r)^n
Future value = Value of $2500 at the end of 5th year = ?
P = present balance in saving account = $2500
r = rate of return = 9% p.a. i.e.0.0075 per month
n = number of compounding months = 5 years * 12 = 60
Future value = 2500 x (1+0.0075)^60
Future value of $2500 at the end of 5th year = $3,914.20
Step 2 - We have to get a equal monthly deposit required to reach a goal of $6085.80 ($10000 - $3914.20)
We can use the future value of annuity formula to know the answer.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = $6085.80
P = monthly deposit required = ?
r = rate of return = 9% p.a. i.e.0.0075 per month
n = number of compounding months = 5 years * 12 = 60
6085.80 = P x {[(1+0.0075)^60 -1]/0.0075}
6085.80 = P x 75.42414
P = 6085.80 / 75/42414
P = 80.69
Monthly deposit required to reach goal = $80.69