# Thread: calculating the number of compounding periods

1. ## 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

2. 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.

3. ## solving for n

the final step is to solve for the exponent as in sqare root it right?

4. 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)

5. Formula that i learned for solving for n

n = LOG ( 10707.16/9380.24 ) / LOG ( 1 + 0.0225 )

6. Yes, that's the formula I gave you; but not .0225; .07/4 = .0175