Question

On your tenth birthday, you received $100 which you invested at 4.5% interest. That investment is now worth $300. How old are you today?

Answer 1

Given,

Amount invested = $100

Interest rate (r) = 4.5% or 0.045

Future value = $300

Solution :-

Let number of years be 'n'

Future value = Amount invested x (1 + r)ⁿ

$300 = $100 x (1 + 0.045)ⁿ

$300/$100 = (1.045)ⁿ

3 = (1.045)ⁿ

Taking 'Log' both sides,

Log(3) = Log(1.045)ⁿ

Log(3) = n.Log(1.045)

1.0986122887 = n.(0.044016885417)

1.0986122887/0.044016885417 = n

24.96 = n

Your age = 24.96 + 10 = 34.96 years

Thus, you are 34.96 years old.