Question

You have a choice: you can keep $5000 under your mattress for the next 50 years, or you can invest it in an account earning 5% interest compounded monthly for 50 years. Compare the amount after 50 years.

Answer 1

Case 1: When you keep $5000 under your mattress for the next 50 years

Total amount after 50 Years: $5000

Case 2: When you invest $5000 at an interest rate of 5% compounded monthly for 50 years.

The formula for Calculating the compound interest

P is the principal amount

r is the rate of interest

t is the time

A is the total amount after time t

In Our case, P = $5000, r = 5% = 0.05

t = 50 years (i.e. 50 * 12 = 600 Months)

Therefore the total amount will be

A = 5000*((1+0.05)^(600)) = 5000*((1.05)^(6000)) = 5000 * (5.17105 * 10^12) = $25,855.25 * 10^12

It is clear that the amount in case 2 is much much higher than that of case 1.