Question

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.

Answer 1

Answer:

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