Question

You invested $12,000 and earned 7.5% interest, which was compunded continuously. If you had $23,568.40 at the end of the investment, how

long was the investment for?

Answer 1

9 years

Explanation:

Formula for continuous compounding is;

Total amount after the compounding period = P + P[(e^(rt)) - 1]

Where;

P = principal

r is interest rate

t is time period of compounding

We are given;

P = $12,000

Interest rate; r = 7.5% = 0.075

Time; t =?

Amount after investment; $23,568.40

Thus;

23568.40 = 12000(1 + [(e^(0.075t)) - 1])

(1 + [(e^(0.075t)) - 1]) = 23568.40/12000

[(e^(0.075t)) - 1] = (23568.40/12000) - 1

[(e^(0.075t)) - 1] = 0.964

(e^(0.075t)) = 1 + 0.964

(e^(0.075t)) = 1.964

0.075t = In 1.964

0.075t = 0.67498

t = 0.67498/0.075

t = 9 years