SOLUTION: John decides to start saving money for a new car. He knows he can invest money into an account which will earn 6.5% APR, compounded weekly, and would like to have saved $10,000 aft

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Question 996999: John decides to start saving money for a new car. He knows he can invest money into an account which will earn 6.5% APR, compounded weekly, and would like to have saved $10,000 after 5 years.
He invested $7226.74 into the account so that he has $10,000 after 5 years.
Determine the APY (Annual Percent Yield) for the account.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
apy is equivalent to the effective interest rate as far as i can tell.

the effective interest rate is equal to:

(1+(r/c)^c - 1

r is the nominal interest rate.
c is the number of compounding periods per year.

in your problem.

r = 6.5% / 100 = .065
c = 52 compounding periods per year (weekly compounding).

your apy is equal to (1 + .065/52) ^ 52 - 1

this becomes equal to 1.00125^52 - 1 = .067115708

that's the effective annual interest rate also known as the apy.

multiply that by 100 and you get 6.7116708%.

here's a reference on apy.

http://www.financeformulas.net/Annual_Percentage_Yield.html