Math Help - Continous compounding question

1. 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!

2. 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?!

3. 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

4. Re: Continous compounding question

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

5. Re: Continous compounding question

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.