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Question 1033292: Using the present value formula to determine the amount to be invested now, or the present value when needed. The desired accumulated amount is $4200. after 9 years invested in an account with 4% interest compounded quarterly.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the discrete compounding 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.
since the number of compounding periods per year is 4, you would ....
divide the annual interest rate by 4.
multiple the number of year by 4.
you will get the interest rate per quarter and the number of quarters.
4% per year compounded quarterly becomes .04 compounded quarterly becomes .04/4 = .01 per quarter.
9 years * 4 = 36 quarters.
f = p * (1+r)^n becomes f = p * 1.01^36
you are given that f = 4200.
the formula becomes 4200 = p * 1.01^36
divide both sides of this equation by 1.01^36 to get 4200 / 1.01^36 = p
solve for p to get p - 4200 / 1.01^36 = 2935.484788.
to see if this is correct, replace p with 2935.484788 in your original equation after you adjusted for the time periods to get:
4200 = 2935.484788 * (1.01)^36.
you will get 4200 = 4200.
this confirms your solution is correct, assuming you constructed your interest rate per time period correctly and your number of time periods correctly.
since these were constructed correctly, your solution is confirmed to be good.
your solution is the present value required is 2935.484788.
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