Question

Your wealthy uncle established a $ 3,000 bank account for you when you were born. For the first 9 years of your life, the interest rate earned on the account was 4%. Since then, rates have been only 2%. Now you are 23 years old and ready to cash in. How much is in your account?

Answer 1

Formula for compound interest can be used to compute the fund size now as:

A = P x (1 + r/n) ^nt

A = Value of investment including interest

P = Principal = $ 3,000

r = Rate of interest = 4 % for 9 years and 2% for rest years

n = No. of compounding in a year = 1

t = No. of years = 23

A = $ 3,000 x (1+0.04)⁹ x (1+0.02) ^{(23 -9)}

   = $ 3,000 x (1.04)⁹ x (1.02) ¹⁴

   = $ 3,000 x 1.423311812 x 1.319478763

   = $ 5,634.089129 or $ 5,634.09

The account has $ 5,634.09 now.