Question

Eight Years ago, Larry invested 6000 into a mutual fund which Compounds continuously. Today, Larry's mutual fund is worth 8500. What is the annual rate of return, stated as a percentage for Larry's investment? Show all work.

Answer #1

Formula for continuous compounding:

A = P e ^{rt}

A = Future value of investment = $ 8,500

P = Principal = $ 6,000

e = Mathematical constant = 2.71828 (Approx.)

r = Rate of interest

t = Time in years = 8

Substituting the values on the above formula, we get,

$ 8,500 = $ 6,000 x 2.71828 ^{8r}

2.71828 ^{8r} = $ 8,500 / $ 6,000

2.71828 ^{8r} = 1.4166666667

Taking logarithm of both sides and solving for r, we get:

8r x log 2.71828 = log 1.4166666667

8r x 0.43429418977 = 0.15126767534

8r = 0.15126767534/0.43429418977

8r = 0.348306928582468

r = 0.348306928582468/8

r = 0.0435383660728084 or **4.354 %**

Annual rate of return is for Larry’s investment is 4.354 %

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