Question

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.)

Answer 1

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,
1.02⁴ⁿ = 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

Answer 2

Still not sure what the answer is.