SOLUTION: In purchasing a house worth 30,000 dollars cash, a man pays 10,000 dollars cash and agreess to make equal payments at the end of each 3 months for 12 years, to discharge all princi

Question 1167593: In purchasing a house worth 30,000 dollars cash, a man pays 10,000 dollars cash and agreess to make equal payments at the end of each 3 months for 12 years, to discharge all principal amd interest at 8% compounded quarterly. Find his periodic payments.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula to use is:

ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.

when you compound quarterly, the number of time periods = number of years * 4 and the interest rate per period = the interest rate per year / 4.

multiply number of years by 12 to get number of quarters.
divide the yearly interest rate by 4 to get the quarterly interest rate.

you get:

p = 20,000
n = 4 * 12 = 48
r = .08 / 4 = .02

and the equation becomes:

a = (20000*.02)/(1-(1/(1+.02)^48))

solve for a to get a = 652.0367109

round to 2 decimal places to get a = 652.04.

that's the payment made at the end of each quarter for 12 years.

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