Question

The total amount of money in a savings account after t years is given by the function A=1000(1.023)t .

How could this function be rewritten to identify the monthly interest rate?

What is the approximate monthly interest rate?



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Function Monthly interest rate

Answer 1

consider the general annual compound interest formula A = P(1+r)^t where P is the principal, r is the annual interest rate, t is # of years, and A is final amount after t years. Compare this general form to your equation to figure out your r-value. To convert from that annual r-value to a monthly r-value, simply divide r by 12 months.

To convert the annual interest rate to a monthly interest rate, simply take your equation, use the monthly interest rate as r instead of the original r, and 12t instead of t as the exponent, since a monthly interest implies the interest compoudns 12 times annually.