Answer:
Each Deposit is $228.2
Step-by-step explanation:
First we need to calculate the effective Interest rate
Effective annual interest rate = [ 1 + APR/n ]^n - 1
Where
APR = 6.7%
n = months ina quarter = 4 months
Placing values in the formula
Effective annual interest rate = [ 1 + 6.7%/4 ]^4 - 1
Effective annual interest rate = 6.87%
Now calculate the monthly effective rate using following formula
Effective monthly rate = [ 1 + Effective annual interest rate ]^(1/n) - 1
Where
n = Months in a year = 12 years
Placing values in the formula
Effective monthly rate = [ 1 + 6.87% ]^(1/12) - 1
Effective monthly rate = 0.55523%
Use following formula to calculate the amount of each deposit
Balance after 7 months of last deposit = Future value of annuity x ( 1 + r )^7
Balance after 7 months of last deposit = [ Monthly deposit x ( 1 + r )^n - 1 / r ] x ( 1 + r )^7
where
Balance after 7 months of last deposit = $8,000
r = 0.55523%
n = 31 months
Placing values in the formula
$8,000 = [ Monthly deposit x ( 1 + 0.55523% )^31 - 1 / 0.55523% ] x ( 1 + 0.55523% )^7
$8,000 = [ Monthly deposit x 33.726 ] x 1.03952
$8,000 / 1.03952 = Monthly deposit x 33.726
$7,695.86 = Monthly deposit x 33.726
Monthly deposit = $7,695.86 / 33.726
Monthly deposit = $228.19