Question 1023852: Solve for future value or present value.
The Downers Grove YMCA had a fund-raising campaign to build a swimming pool in 6 years.Members raised $825,000; the pool is estimated to cost $1,230,000. The money will be placed in Downers Grove Bank, which pays daily interest at 6%. Will the YMCA have enough money to pay for the pool in 6 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can't possibly mean daily interest.
you must mean annual interest compounded daily.
that would make more sense.
i'll assume that.
the general formula is:
f = p * (1 + r)^n
f is the future value which is what you want to find.
p is the present value which is 825k.
k means to multiply the value shown by 1000.
1230k is therefore equal to 1,230,000.
825k is therefore equal to 825,000.
r is the interest rate per time period.
since the interest rate is 6% annually, and the time period is days, then you would divide 6% by 360, because 360 is, i believe, the number of days in a year for financial analysis purposes.
you might also have used 365 days, or 365.25 days, but i believe the answer will be sufficient close either way.
i'm using 360.
if you know you should be using something else, then by all means, reproduce the analysis using those number of days.
r is equal to .06 / 360 = .000166666667 per day.
n is equal to the number of days.
6 years * 360 days per year is therefore equal to 2160 days.
the formula of f = p * (1 + r)^n becomes:
f = 825k * (1.000166666667)^2160.
solve for f to get f = 1182.461297k.
since you need 1230k, you would not have enough.
if you used 365 days instead of 360 days, the answer would have been extremely close to what is already shown.
still not enough.
the most frequent compounding you can do is continuous compounding.
the formula for that is f = p * e^(rt).
r is .06 per year.
t is 6 years.
with continuous compounding, your formula becomes f = 825k * e^(.06*6).
f then becomes equal to 1182.496767.
still not enough, and you can't compound any more frequent than continuous compounding.
that's equivalent to compounding every minute or every second or every millionth of a second.
there is a limit to how much higher your value will be with more numerous compounding.
that limit is continuous compounding.
bottom line is you won't have enough, even if you used continuous compounding, IF you meant 6% a year compounded daily.
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