Question

The total amount of money in a savings account after t years is given by the function A=1000(1.031)^t . How could this function be rewritten to identify the monthly interest rate? What is the approximate monthly interest rate?

Answer 1

Hi There!

Explanation:

Compound Interest: a = p(r/n + 1)^nt

Function: A=1000(1.031)^t

1.031 - 1 = 0.031 = 3.1%

a = 1000(0.031/12 + 1)^12t

a = 0.0025833333333333333333333333333333333333...

Answer:

0.002583...

Hope This Helps :)

Answer 2

A = 1000 ( 1 + .031/12) ^(12t)

The approximate monthly interest rate is .2583 percent

Explanation:

A=1000(1.031)^t

The formula for compound interest is given by

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

Take 1.031 and subtract 1

.031 is the yearly rate in decimal form

A = 1000 ( 1 + .031/12) ^(12t)

Change to a percent = 3.1 %

Divide by 12

3.1/12 = .2583333333(repeating) %

This would be the monthly rate