# calculating the number of compounding periods

• Mar 16th 2010, 01:37 PM
diehardmath4
calculating the number of compounding periods
\$7500 was borrowed for a 4 year term at 9% compounded quarterly.The terms of the loan allow prepayment of the loan based on discounting the loan's maturity value at 7% compounded quarterly How long ( to the nearest day ) before the maturity date was the loan prepaid if the payout amount was \$9380.24 including accrued interest ? for the puropese of determining the number of days in a partial calendar quarter, assume that a full quarter has 91 days.

FV = 9380.24
PV = 7500
n =
i = ( confused on )
n = ?

because of the 7% ccompounded quarterly and 9 % compounded quarterly both of them threw me off so i am stuck
• Mar 16th 2010, 06:20 PM
Wilmer
Step#1:
7500(1 + .09/4)^16 = 10,707.16 : that's the initial FV
Step#2:
10707.16 / (1 + .07/4)^n = 9380.24
Solve for n ; that'll be the number of quarters.

Let us know if you need more help.
• Mar 26th 2010, 05:30 PM
diehardmath4
solving for n
the final step is to solve for the exponent as in sqare root it right?
• Mar 26th 2010, 06:57 PM
Wilmer
Quote:

Originally Posted by diehardmath4
the final step is to solve for the exponent as in sqare root it right?

I told you, just solve this for n:
10707.16 / (1 + .07/4)^n = 9380.24

Example:
if a / x^n = b, then n = log(a/b) / log(x)
• Mar 27th 2010, 09:17 AM
diehardmath4
Formula that i learned for solving for n

n = LOG ( 10707.16/9380.24 ) / LOG ( 1 + 0.0225 )
• Mar 27th 2010, 11:58 AM
Wilmer
Yes, that's the formula I gave you; but not .0225; .07/4 = .0175