Question 1097941
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.