# Continous compounding question

• Sep 17th 2011, 12:10 AM
Redeemer_Pie
Continous compounding question
Hello all, I am working out a question at the moment and im not too sure if it is write or wrong. Hope someone can help thanks!! the question goes like this: A loan of 100K is taken out and n.interest is 8 percent. Firstly i found that if the loan is to repaid within 12 years the answer i got was 1082. The problem i have at the moment is this: "If the monthly repayment are continuosly repaid over 12 years, what is the size of the monthly repayment?" I worked it out to be roughly 3000. Can anyone confirm this? Not too sure if this is right. Thanks!
• Sep 17th 2011, 07:26 AM
Wilmer
Re: Continous compounding question
1082 (1082.45258...) is correct IF the rate is 8% annual compounding monthly.

Do you realise that 3000 * 144 = \$432,000; are you willing to repay that if you borrow only \$100,000?!
• Sep 17th 2011, 09:20 PM
Redeemer_Pie
Re: Continous compounding question
I will restate the question again, since there is a mistype.

"If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"

Thanks
• Sep 18th 2011, 02:11 AM
dexteronline
Re: Continous compounding question
Quote:

Originally Posted by Redeemer_Pie
I will restate the question again, since there is a mistype.
"If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"
Thanks

PVA = \$100,000
N = 12x12 = 144
I = 8%/12 = 0.666666667%

Continuous Compounding of Interest

PVA = R x PVIFA(8%/12,144)

PVIFA(8%/12,144) = [1 - e^(-in)] / [e^i - 1.0]
PVIFA Continuous Compounding Calculator

PVIFA(8%/12,144) = [1 - e^(-8%/12*144)] / [e^(8%/12) - 1.0]
PVIFA(8%/12,144) = 92.2578563838

R = PVA/PVIFA(8%/12,144)
R = 100000/92.2578563838
R = \$1083.92

Discrete Compounding of Interest

PVA = R x PVIFA(8%/12,144)

PVIFA(8%/12,144) = [1 - (1+i)^-n]/i
PVIFA Discrete Compounding Calculator

PVIFA(8%/12,144) = [1 - (1+0.6666666667%)^-144]/0.6666666667%
PVIFA(8%/12,144) = [1 - (1.06666666667)^-144]/0.06666666667
PVIFA(8%/12,144) = 92.3827995

R = PVA/PVIFA(8%/12,144)
R = 100000/92.3827995
R = \$1082.45
• Sep 18th 2011, 04:02 AM
Wilmer
Re: Continous compounding question
Quote:

Originally Posted by Redeemer_Pie
I will restate the question again, since there is a mistype.
"If the monthly repayments are continously compounded over a 12yr period, calculate the size of the monthly repayment"

It's the INTEREST that continuously compounds, NOT the repayments.