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Question 1097941: Which of the following has a lower present value?
$90,000 if interest is paid at a rate of 5.44% compounded continuously for 2 years
$96,000 if interest is paid at a rate of 3.4% compounded continuously for 29 months
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! continuous compounding formula is f = p * e^(r*n)
f is the future value
p is the present value
r id the interest rate per time period
n is the number of time periods.
solve for p to get:
p = f / e^(r*n)
the one thing that you have to do is to keep the time periods consistent.
if your interest rate is in time periods and your number of time periods are different, you will not get the right answer.
first problem gets you:
f = 90,000
p = what you want to find.
r = .0544 per year
n = 2 years.
time periods are the same so just solve.
p = f / e^(r*n) becomes p = 90,000 / e^(.0544*2).
this gets you p = 80721.88034
second problem gets you:
f = 96,000
p = what you want to find.
r = .034 per year
n = 29 months.
you either have to convert interest rate per year to months or you have to convert months to years.
converting months to years, you get:
f = 96,000
p = what you want to find.
r = .034 per year
n = 29/12 years
you get p = 96,000 / e^(.034 * 29/12).
this gets you p = 88427.36891
converting interest rate per year to interest rate per month, you get:
f = 96,000
p = what you want to find.
r = .034/12 per month
n = 29 months
you get p = 96,000 / e^(.034/12 * 29)
this gets you p = 88427.36891
keeping the rate per time period and the number of time periods consistent is the key.
so, first one gets you p = 80721 and second one gets you p = 88427.
first one gets you the smaller present value.
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