SOLUTION: You owe your parents $27,000 (in present day dollars) and want to repay them in equal amounts the first to occur in 3 years from today and the other in 8 years from today. If the i

Question 1161014: You owe your parents $27,000 (in present day dollars) and want to repay them in equal amounts the first to occur in 3 years from today and the other in 8 years from today. If the interest rate is 6.1% per annum compounding monthly, what will be the amount of each repayment?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to make this easier for you to see, i've assigned letters to the numbers.
you can then replace the letters with numbers to determine for yourself that the answer is the answer i gave you.

let a = (1 + .061/12) ^ 36
let b = (1 + .061/12) ^ 96
let x = the amount you are looking for.

x/a is the present value of the payment in the 48th month (4th year).
x/b is the present value of the payment in the 96th month (8th year).

your formula is x/a + x/b = 27000.
multiply both sides of this formula by a*b to get:
a*b*x/a + a*b*x/b = a*b*27000
simplify to get:
b*x + a*x = a**b*27000
factor out the x on the left side of the equation to get:
x*(a+b) = a*b*27000
divide both sides of the equation by (a+b) to get:
x = a*b*27000/(a+b)

your answer will be 18649.41705

that's the payment in the 48th month and the 96th month that will satisfy the 27000 loan.

the present value of that for 36 months = 18649.41705 / (1 + .061/12) ^ 36 = 15537.84162.
the present value of that for 96 months = 18649.41705 / (1 + .061/12) ^ 96 = 11462.15838.
their sum = 27000 which is the present value of the loan.

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