Question

Assume you have a saving account that pays 4% APR. If you have a beginning balance of$6000, How much do you need to save on a monthly basis in a saving account (add to your saving account) to have a down payment of $20000 for a house in 5 years

Answer 1

Step 1 - Calculation the future value of beginning balance in saving account in 5 years
We can use the Future value of lumsum formula to calculate this value.
Future value of lumsum = P x (1+r)^n
Future value of lumsum = future value of beginning balance in saving account in 5 years = ?
P = beginning balance in saving account = $6000
r = monthly interest rate = 4%/12 = 0.0033
n = number of months (i.e.compounding periods) = 5 years x 12 = 60
Future value of lumsum = 6000 x (1+0.0033)^60
Future value of lumsum = 6000 x 1.220997
Future value of lumsum = 7325.98
Future value of beginning balance in saving account in 5 years = $7,325.98
Step 2 - Calculation of monthly savings
Future value of monthly savings = Down payment required in 5 years - Future value of beginning balance in saving account
Future value of monthly savings = $20,000 - $7,325.98 = $12,674.02
So, we need to calculate the monthly savings which will result into future value of $12,674.02 in 5 years.
We can use the Future value of annuity formula to calculate the monthly savings.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = 12674.02
P = monthly savings = ?
r = monthly interest rate = 4%/12 = 0.0033
n = number of months (i.e.compounding periods) = 5 years x 12 = 60
12674.02 = P x {[(1+0.0033)^60 -1]/0.0033}
12674.02 = P x 66.29898
P = 191.16
Monthly savings = $191.16
You need to save $191.16 on a monthly basis in a saving account to have a down payment of $20000 for a house in 5 years.