Question 1100973: Find the number of years it will take for $28,000 to grow to $29,718 at 6% interest compounded quarterly Found 3 solutions by josgarithmetic, ikleyn, greenestamps:Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website! Let n be number of compounding periods ( one fourth of a year each ).
The formula is
FV =
where FV is the Future Value, A is the original amount ($28,000), 0.06 = 6%, 4 (four) is the number of quarters in the year
and n is the number of years.
The table is
n, year FV
0 28000.00
1 29718.18
2 33477.31
Answer. Exactly one year.
The solution, the calculations and the answer by @josgarithmetic ("A little more than 9 years 11 months") are W R O N G.
Her answer doesn't make sense. The $28000 at 6% interest for just one year without quarterly compounding would be $29680, so with compounding it will be close to the target value. So the answer should be something close to 1 year.
The annual interest rate is 6%, or .06; the quarterly interest rate is one-fourth of that, or .015. So we need to solve
where n is the number of compounding periods (quarters of a year).
So in fact the answer is that the $29718 value will be reached in 1 year with quarterly compounding.