Posted by **Roger** on Friday, December 3, 2010 at 10:48am.

Please Help.

How long, to the nearest tenth of a year, will it take $12,500 to grow to $20,000 at 6.5% annual interest compounded quartely? (Use the formula for compound interest with n compoundings per year to solve for t.)

- Algebra -
**MathMate**, Friday, December 3, 2010 at 8:02pm
With k compounding a year, the compound interest formula becomes:

FV = PV*R^{kn}

where

FV=future value

PV=present value

r=annual rate of interest, in fraction.

For example, 0.12 stands for 12%.

k=number of compounding a year, 4 for compounding every three months.

n=number of years

R=compounding rate, = 1+r/k

For example,

at 8% annual interest compounded 4 times a year, $10000 will accumulate to $20000 in n years.

20000=10000*(1+0.08/4)^{4n}

divide by 10000,

1.02^{4n} = 2.0

take log on both sides

4n log(1.02) = log(2.0)

n = (1/4)log(2)/log(1.02)

=8.75 years

- Algebra -
**Roger**, Sunday, December 5, 2010 at 7:11pm
Still not sure what the answer is.

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