Kenny opened a sinking fund account and hopes to accumulate $16,000 in 25 months. The yearly interest rate is 7.8%. How much should he invest per month to reach his goal?
Would the answer be 591.58?
i = .078/12 = .0065
n = 25
payment --- P
P( 1.0065^25) - 1)/.0065 = 16000
on my calculator ...
P = 591.48
To find out how much Kenny should invest per month to reach his goal, we can use the formula for the future value of a sinking fund:
FV = PMT * ((1 + r)^n - 1) / r
Where:
FV is the future value, which is $16,000 in this case.
PMT is the monthly investment amount we want to find.
r is the monthly interest rate, which can be calculated by dividing the yearly interest rate by 12. In this case, the yearly interest rate is 7.8%, so the monthly interest rate would be 7.8% / 12.
n is the number of months, which is 25 in this case.
Using these values, we can calculate PMT:
PMT = FV * r / ((1 + r)^n - 1)
Let's plug in the values and calculate:
r = 7.8% / 12 = 0.065
PMT = $16,000 * 0.065 / ((1 + 0.065)^25 - 1)
PMT = $16,000 * 0.065 / (1.065^25 - 1)
Calculating further, we get:
PMT ≈ $591.85
Therefore, Kenny should invest approximately $591.85 per month to accumulate $16,000 in 25 months.