Question

At the end of t years, the future value of an investment of $7000 in an account that pays 7% APR

0.07 12t
compounded monthly is S = 7000(1 + 0.07/12)^12t dollars. Assuming no withdrawals or additional deposit,
how long will it take for the investment to reach $21,000? Round to three decimal places.

Answer 1

it will take approximately 9.546 years for the investment to reach $21,000.

Explanation:

We need to solve for t:

S = 7000(1 + 0.07/12)^(12t) = 21000

Divide both sides by 7000:

(1 + 0.07/12)^(12t) = 3

Take the natural logarithm of both sides:

ln[(1 + 0.07/12)^(12t)] = ln(3)

Use the power rule of logarithms:

12t ln(1 + 0.07/12) = ln(3)

Divide both sides by 12 ln(1 + 0.07/12):

t = ln(3) / [12 ln(1 + 0.07/12)] ≈ 9.546