Question

after ___ years, the investment has doubled. APR=8%, compounding periods=quarterly, time to double=?

Answer 1

Compound interest formula: \[\Large A = P(1 + \frac{ r }{ n })^{nt}\]
Doubled implies A/P = 2; r = 0.08; n = 4 (compounded quarterly)
Solve for t.

Answer 2

how do i do it?

Answer 3

Divide both sides of the formula by P
A/P = (1 + r/n)^nt
Plug in the values:
2 = (1 + 0.08/4)^(4t)
2 = (1.02)^(4t)
take log on both sides:
log(2) = log{ (1.02)^(4t) } = 4t * log(1.02)
divide both sides by 4log(1.02)
log(2) / {4log(1.02) = t
or t = log(2) / {4log(1.02)
use you calculator to compute the right side and round your answer to two decimal places.

Answer 4

9.99

Answer 5

so, it will be 0.95 years?

Answer 6

\[t = \frac{ \log(2) }{ 4*\log(1.2) } = 8.75 years\]

Answer 7

You may want to double-check on your calculator. But at least it is in the ball park of about 9 years which I was expecting based on the doubling time given by the rule of 72.

Answer 8

okay. thanks

Answer 9

you are welcome.