A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by b(x)=625(1.015)x.



The balance in the account increases at what rate per year? Answer by percent,

1 answer

The rate at which the balance in the account increases per year can be found by finding the derivative of the function b(x)=625(1.015)^x with respect to x.

Taking the derivative, we have:
b'(x) = 625(1.015)^x * ln(1.015)

To find the rate as a percent, we multiply b'(x) by 100%:
b'(x) = 625(1.015)^x * ln(1.015) * 100%

Therefore, the balance in the account increases at a rate of approximately 1.54% per year.