# Math

posted by Maria

Andy needs to pay off a loan of \$18,000 in 5 years. Find the amortization payment he would need to make each semi-monthly pay period (twice a month)at 6% compounded bi-monthly, in order to pay off the loan.

1. Reiny

I understand bi-monthly to mean every other month, or 6 times a year.

The main problem here is that the payment period does not coincide with the interest period, so my normal formula does not work

so we will convert the 6% compounded bi-monthly to one of i compounded semi-monthly since the payment period is semi-monthly

so (1+i)24 = (1.-1)^6

take the 24th root of both sides
1+i = 1.01^(6/24) = 1.01^(1/4)
1+i = 1.00249

(check:
1.00249^24 = 1.06152..
1.01^6 = 1.06152.. OK )

let the payment be P
he will make 30 of these

P( 1 - 1.00249^-30)/.00249 = 18000
P = 623.44

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