Determine the accumlated amount for $500 for 13 quarters at 10% compounded quartertly?

Question

Determine the accumlated amount for $500 for 13 quarters at 10% compounded quartertly?

can you please show me the solution, and how do i get the time for 13 quarters...

Answer 1

The formula you need to use is for compound interest compounded n times per year.
Accumulated Value = Principle * (1+r/n)^nt
where r is the annual interest rate, n is the number of compoundings per year, and t is the number of years.
In your case, interest is compounded quarterly, so we need to think in quarters.
Think of r/n as the interest rate per quarter, in this case .10 / 4 = .025
Think of nt as the number of quarters the investment goes for.
Thus the Accumulated Value would be:
500 * (1.025)^13 = $689.26

This is easier than translating 13 quarters into 13/4 = 3.25 years, since you'll then multiply this t by n=4 to get nt = 13.
As soon as you see "compounded nthly" think in terms of "nths of a year" throughout the question and it gets less complicated.

Answer 2

The trick is to think of time in "time periods" in terms of the compounding time. Here, the time is 13 quarters. Each quarter, you earn 0.1/4 or 2.5 percent interest on the sum at the start of the quarter. Then if S is the sum desired:
S = 500 [ 1.025]^13

Answer 3

$1,150.00 altogether. 500*.10=50, 50*13(quarters)=650, 650+500=$1,150.00.

Answer 4

Didn't realize Yahoo Answers was a homework service now.

Answer 5

Just ask the Bank

Answer 6

no