Question

At age 20 you invest $1,900 that earns 9.25 percent each year. At age 35 you invest $1,900 that earns 12.25 percent per year. In which case would you have more money at age 60?

Answer 1

Formula for compound interest can be used to compute future value of investment as:

A = P x (1 + r/m) ^mt

A = Future value of investment

P = Principal

r = Rate of interest

m = No. of compounding in a year

t = No. of years

Computation of future value of $ 1,900 invested at age 20:

P = $ 1,900, r = 9.25 %, m = 1, t = 60 – 20 = 40

A = $ 1,900 x (1+0.0925/1)^1x40

   = $ 1,900 x (1+0.0925)⁴⁰

   = $ 1,900 x (1.0925)⁴⁰

= $ 1,900 x 34.4237219917981

= $ 65,405.0717844163 or $ 65,405.07

Computation of future value of $ 1,900 invested at age 35:

P = $ 1,900, r = 12.25 %, m = 1, t = 60 – 35 = 25

A = $ 1,900 x (1+0.1225/1)^1x25

   = $ 1,900 x (1+0.1225)²⁵

   = $ 1,900 x (1.1225)²⁵

= $ 1,900 x 17.9745796101044

= $ 34,151.7012591983 or $ 34,151.70

Investment of $ 1,900 at age 20 accumulates more money at the age 60.