1. How much would $1,000,000 due in 100 years be worth todayif the discount rate was 5%? if the discount rate was 10%. Discuss how and whythe results are different at the different interest rates.
2. If you wanted to have $600,000 in savings at retirement, how much would you need to save each year over the next 25 years if you could earn 9% annually on your savings?
The future value of an amount with a present value of P, with a discount rate of r, in t years is equal to P/(1+r)^t.
The future value of $1000000 in 100 years with a discount rate of 5% is 1000000/(1+0.05)^100 = 1000000/1.05^100 = $7604.49. If the discount rate is 10%, the future value of the same amount in 100 years is 1000000/(1+0.1)^100 = 1000000/1.1^100 = $72.56
The result is different for different discount rates as the value of money is decreasing at different rates.
If a person saves an amount P every year for n years and the rate of interest is r, the total amount after n years is given by P*((1+r)^n - 1)/r
To collect $600000 after 25 years with an annual interest rate of 9%, the amount to be saved every year is P where P*(1.09^25 - 1)/0.09 = 600000, this gives P = $7083.75