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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Business

Oliver Browning

7 August, 21:13

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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Diamond Myers · 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.