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?

Question

Clay Blankenship

Business

11 March, 15:58

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?

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Answers (1)

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Konnor Carpenter · Answer 1

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.