Question

You have $10,000 to invest for the next 40 years for your retirement. You are offered an investment plan that will pay you 5% per year for the next 20 years and 10% for the last 20 years. How much will you end up with in 40 years’ time? Does it matter if the investment plan pay you 10% for the first 20 years and 5% for the next 20 years? Why or why not?

Answer 1

Future Value = Present Value * ( 1 + Interest rate ) ^ Number of year

Future Value = 10,000 * ( 1 + 5%)^20 * ( 1 + 10%)^20

= 10,000 * (1.05)^20 * (1.10)^20

= 10000 * 2.65329 * 6.72749

= 178499.8194

So, The Future Value =  178499.8194

No, If the interest rate for the period is same and the total number of years are same then the amount at the end of both the priod will be same.

If the interest rate is 10% for first 20 Year and 5% afterward for next 20 Years.

Future Value = 10,000 * ( 1 + 10% )^20 * ( 1 + 5%)^20

= 10000 * 6.72749 * 2.65329

= 178499.819

As, We can see that the amount at the end of period is same.