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

A = 1000(1 + 0.023)^12t

A = 1000(1.023^12)^t/12

A = 1000(1.023^t/12)^12t

0.23%

0.19%

0.31%

Answer 1

A=1000(1.023112)^12t 0.19%

Answer 2

`A=1000(1+(0.023)/(12))^(12t)`

Rate of interest (r) = 0.19% monthly

Explanation:

Given: The total amount of money in a saving account after t years.

`A=1000(1.023)^t`

Formula:

`A=P(1+r)^t`

Now we compare this formula with with given model.

P=1000

Rate of interest annually (r) = 0.023

Time = t

We need to change into monthly interest

New rate will divide by 12

New time will multiply by 12

`r=(0.023)/(12)=0.0019`

`t=12* t =12t`

Function for monthly rate

`A=1000(1+(0.023)/(12))^(12t)`

Rate of interest (r) = 0.19% monthly

`\text{Thus, Function Monthly interest rate: }A=1000(1+(0.023)/(12))^(12t)\text{ and Monthly Interest rate }= 0.19\%`