Question

How many years will it take for an initial investment of $ 50 comma 000 to grow to $ 75 comma 000 question mark Assume a rate of interest of 5​% compounded continuously

Answer 1

It will take approximately 8.31 years or 8 years and 4 months to earn $75,000 by investing $50,000 at 5% compounded continuously.

Step-by-step explanation:

Compound of interest is the addition of interest value in principal amount to calculate further interest on the interest and principal amount as well. It other words it is Interest on Interest situation. Reinvesting of interest value is the concept behind this.

We use following formula to calculate the period required to earn compounded value.

Future Value = Present value ( 1 + rate of Interest )^number of period

$75,000 = $50,000 x ( 1 + 0.05 )^n

$75,000 / $50,000 = ( 1.05 )^n

1.50 = 1.05^n

log 1.50 = n log 1.05

n = log 1.5 / log 1.05

n = 8.31

Answer 2

It will take 8 years and 113 days.

Step-by-step explanation:

Giving the following information:

How many years will it take for an initial investment of $50,000 to grow to $75,000.

We need to use a variation of the future value formula:

FV= PV*(1+i)^n

Isolation n:

n=[ln(FV/PV)]/ln(1+r)

n= [ln(75000/50,000)] / ln(1.05)= 8.31

To be more accurate:

0.31*365= 113

It will take 8 years and 113 days.