Answer to Question #241617 in Accounting for Manish Kumar

Question

When Y was born, a bank account was started in Y’s name with $20.05 The account has earned an average annual rate of return of 4%. Today, the account is valued at $500.00. How old is Y?

Answer 1

Calculation of the age of Y:

The age of Y will be equal to the time it will take $20.05 to grow to $500 at the average annual rate of return of 4%:

Formula,

$Future value = Present value x (1+ rate)^n$

$500 = 20.05 x (1+ 0.04)^n$

$500 / 20.05 = (1.04)^n$

$24.937656 = (1.04)^n$

Apply log both the side,

$Log(24.937656) = Log(1.04)^n$

$Log(24.937656) = nLog(1.04)$

$n = Log(24.937656) / Log(1.04)$

$n = 1.396856 / 0.017033$

$n = 82$

So, it will take 82 years to $20.05 to grow to $500 at the average annual rate of return of 4%. Hence, Y is 82 years old now.