In order to have a future value of $50,000 in 10 years, determine how much money you would be required to pay annually if your interest rate is 5 percent per year. (1 point)
To calculate the annual payment required to achieve a future value of $50,000 in 10 years at a 5% interest rate, we can use the formula for calculating the future value of an annuity.
FV = Pmt * [(1 + r)^n - 1] / r
Where:
FV = Future Value ($50,000)
Pmt = Annual Payment
r = Interest Rate (5% or 0.05)
n = Number of Years (10)
Substitute the known values into the formula and solve for the annual payment (Pmt):
$50,000 = Pmt * [(1 + 0.05)^10 - 1] / 0.05
$50,000 = Pmt * [1.6288946267774424 - 1] / 0.05
$50,000 = Pmt * 0.6288946267774424 / 0.05
$50,000 = Pmt * 12.577892535548849
$50,000 / 12.577892535548849 = Pmt
$3,973.20 = Pmt
Therefore, you would be required to pay approximately $3,973.20 annually in order to achieve a future value of $50,000 in 10 years at a 5% interest rate.