SOLUTION: What is the equation for this problem: Determine the amount of an investment if 500 $ is invested at an interest rate of 4.25% compounded quarterly for 12 years

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Question 1190965: What is the equation for this problem: Determine the amount of an investment if 500 $ is invested at an interest rate of 4.25% compounded quarterly for 12 years
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the equation is f = p * (1 + r) ^ n
f is the future value
p is the present value
r if the interest rate per time period.
n is the number of time periods.

4.25% per year compounded quarterly is equal to 4.25/4 = 1.0625% per quarter.
12 years * 4 quarters per year = 48 quarters.
the growth rate is equal to 1.0625% / 100 + 1 = 1.010625 per quarter.
this means that 1 + r = 1.010625
the formula becomes:
f = 500 * 1.010625 ^ 48 = 830.4085123.

this might be a little cryptic, so i'll give you the same info in a slightly different way.
the formula is f = p * (1 + r) ^ n
the time periods are in quarters.
the annual growth rate is 4.25% / 100 = .0425.
when compounded quarterly, you take the annual growth rate and divide it by 4 to get a quarterly growth rate of .0425 / 4 = .010625 per quarter.
n = 12 years * 4 quarters per year = 48 quarters.
the formula becomes:
f = 500 * (1 + .010625) ^ 48 = 830.4085123.

i'll be available to answer any questions or concerns you might have about this.