How long will it take for a $4000 investment to grow to $6000 at an annual rate of 15%, compounded monthly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth.

It will take 2.72 years and 32.64 months.

Explanation:

Future value is the sum of principal amount and compounded interest amount invested on a specific rate for a specific period of time.

Use following formula to calculate the time period.

FV = PV x (1 + r) ^n

FV = Future value = $6,000

PV = Present Value = $4,000

r = rate of interest = 15% yearly = 15% / 12 = 1.25%

n = time period = ?

$6,000 = $4,000 x (1 + 1.25%) ^n

$6,000 = $4,000 x (1.0125) ^n

$6,000 / $4,000 = (1.0125) ^n

1.5 = (1.0125) ^n

Log 1.5 = n log 1.0125

n = Log 1.5 / log 1.0125

n = 32.64 months

n = 2.72 years