So you can retire early, you have decided to start saving $500 a month starting one month from now. You plan to retire as soon as you can accumulate $1 million. If you can earn 5 percent on your savings, how many years will it be before you can retire?

It will take him 45 years

Explanation:

In this question, we are asked to calculate the number of years it would take to accumulate $1,000,000 if there is a plan to save $500 per month at an interest rate of 5%.

To solve this, we use the following mathematical formula:

Future value of annuity = Annuity payment * { (1+r) ^n - 1}/r

Where r is the monthly interest rate and n is the number of months it will take.

From the question, we can identify the following;

Since he earns 5% interest on savings, the actual monthly interest rate will be 5%/12 = 0.4167% = 0.004167

Annuity payment = monthly payment = $500

Future value of annuity = $1,000,000

We substitute these values into the equation:

1,000,000 = 500 * [ (1+0.004167) ^n - 1]/0.004167

8.334 = (1.004167) ^n - 1

1+8.334 = (1.004167) ^n

9.334 = (1.004167) ^n

To get n, we simply take the log on both sides of the equation

Log 9.334 = nLog 1.004167

n = Log9.334/Log1.004167

n = 537 months

Question asks to calculate in years

there are 12 months in a year. The number of years it will take will be 537/12 = 44.76 years and that's approximately 45 years