SOLUTION: Jill borrows $14,000 from you today. She agrees to repay you in two equal amounts, the first to occur in 4 years from today and the other in 8 years from today. If the interest rat

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Question 1161013: Jill borrows $14,000 from you today. She agrees to repay you in two equal amounts, the first to occur in 4 years from today and the other in 8 years from today. If the interest rate is 14.0% per annum compounding monthly, what will be the amount of each repayment?
Answer by Theo(13342) (Show Source):
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let a = (1 + .14/12) ^ 48
let b = (1 + .14/12) ^ 96
let x = the payment that will be payed back in 4 years and then in 8 years at 14% per year compounded monthly.
the amount owed is 14000.
the formula is x/a + x/b = 14000
multiply both sides of this equation by a*b to get:
a*b*x/a + a*b*x/b = a*b*14000
simplify to get:
b*x + a*x = a*b*14000
factor out the x to get:
x*(a+b) = a*b*14000
divide both sides of this equation by (a+b) to get:
x = a*b*14000/(a+b)
solve for x to get:
x = 15530.26616.
that's the payment to made at the end of the 4th year and the 8th year.
that divided by (1 + .14/12)^48 = 8899.830705 = the present value of that payment.
that divided by (1 + .14/12)^96 = 5100.1692975 = the present value of that payment.
their sum is 14000 which is the present value of the money that is owed, satisfying the debt.