You have $50,000 in savings for retirement in an investment earning a stated annual rate of 11% compounded monthly. you aspire to have $1,000,000 in savings when you retire. assuming you add no more to your savings, how many years will it take to reach your goal?

2,39 years

Explanation:

Compound interest formula :

Final Capital(FC)= Initial Capital(IC) (1+ interest(i))^(number of periods)(n)

The problem is giving us:

FC = $1,000,000

IC =$50,000

i= 11% (periodic rate: monthly)

And we want to find n. Because the interest rate is given in months we will first find n in number of months. Then, we will get the number of years.

If we transform the formula in terms of FC, FI and i, we get:

n= [ln(FC/IC)]/[ln(1+i)]

n=ln(20)/ln(1.11)

n=28,706 months

We divide 28,706 into 12 (12 months in a year),  we get 2,39 years.