Answer:
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
