Henry wishes to accumulate $4,500 in 2 years for a long vacation. Find the sinking fund payment he
would need to make each month, at 6% compounded monthly
To calculate the sinking fund payment Henry would need to make each month, we can use the formula for the future value of a sinking fund:
PV = PMT * [(1 + r)^n - 1] / r
Where:
PV = Present Value (starting amount)
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, Henry wants to accumulate $4,500 in 2 years. The interest rate is 6% compounded monthly.
First, let's convert the annual interest rate into a monthly rate. Since interest is compounded monthly, we divide the annual rate by 12:
r = 6% / 12 = 0.06 / 12 = 0.005
Next, we substitute the given values into the formula:
PV = $0 (assuming no initial amount)
PMT = ?
r = 0.005
n = 2 * 12 = 24 (since there are 12 months in a year)
$0 = PMT * [(1 + 0.005)^24 - 1] / 0.005
We need to solve for PMT, so we rearrange the formula:
PMT = $0 / [(1 + 0.005)^24 - 1] / 0.005
Following the order of operations, we calculate the numerator first:
Numerator = [(1 + 0.005)^24 - 1] / 0.005 = 1.13399
Now we can calculate the sinking fund payment per month:
PMT = $4,500 / 1.13399
PMT ≈ $3,966.72
Therefore, Henry would need to make monthly sinking fund payments of approximately $3,966.72 to accumulate $4,500 in 2 years at a 6% interest rate compounded monthly.