Question

How long will it take an investment of $2000 to double if the investment earns interest at the rate of 4%/year compounded monthly? (Round your answer to one decimal place.

Answer 1

Compound Interest Formula:   

A = P(1 + r/n)^(n·t)

A = final amount = $4000.00   

P = beginning amont = $2000.00

t = time (in years)

r = rate (as a decimal) = 4/100=0.04

n = number of compounding periods per year = 1

---> 4000 = 2000(1 + 0.04/1)^(t·1)

---> 4000 = 2000(1.04)^t

---> 2 = (1.04)^t

---> log(2) = log(1.04)^t

Now, since exponents come out as multipliers:

---> log(2) = t·log(1.04)   

Divide both sides by log(1.04):

log(2)/log(1.04)=t

t=log(2)/log(1.04)

t=0.3010/0.0170

t=17.705

t=17.7

Therefore it will take 17.7 years approximately to double the invesment.