Question 1104798: If a bank pays 2% compounded quarterly, how much should be deposited now to have $10,000
(a) 5 years later (b) 10 years later
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2% per year / 100 = .02 per year interest rate.
.02 interest rate per year compounded quarterly is equal to .005 interest rate per quarter.
5 years * 4 quarters per year = 20 quarters.
10 years * 4 quarters peryear = 40 quarters.
your time period is quarters of a year.
the formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
in your first problem:
p is what you want to find.
f is equal to 10,000 dollars.
r is equal to .005
n is equal to 5.
formula becomes 10,000 = p * (1 + .005) ^ 20
divide both sides of this equation by (1 + .005) ^ 20 to get 10,000 / (1 + .005) ^ 20 = p
solve for p to get p = 9050.629043.
confirm by replacing p in the formula of f = p * (1 + r) ^ 20 to get f = 9050.629043 * (1 + .005) ^ 20.
solve for f to get f = 10,000, confirming the solution is good.
in your second problem, the formula of f = p * (1 + r) ^ n becomes:
10,000 = p * (1 + .005) ^ 40.
solve for p to get p = 10,000 / (1 + .005) ^ 40 = 8191.388607.
confirm by replacing p in the formula of f = p * (1 + r) ^ 40 to get f = 8191.388607 * (1 + .005) ^ 40.
solve for f to get f = 10,000, confirming the solution is correct.
if you are given the annual rate percent, you have to divide by 100 to get the annual rate.
in this case 2% was divided by 100 to get .02.
you then divide the annual rate by the number of compounding periods per year to get the rate per compounding period.
in this case .02 was divided by 4 to get a quarterly rate of .005.
you then take the number of years and multiply them by the number of compounding periods per year.
in this case 5 years became 20 quarters and 10 years became 40 quarters.
your solution for (a) is 9050.629043
your solution for (b) is 8191.388607
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