Question

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

Answer 1

Answer:

The total amount of money in a saving account after t years is given by:

$A = 1000(1.023)^t$

we can write this function as;

$A = 1000(1+0.023)^t$             .....[1]

Use the formula:-

$A = P(1+\frac{r}{n})^{nt}$ ; where

P = Principal amount (the initial amount borrow or deposit)

r= annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A =amount of money accumulated after n years, including interest.

n = number of times the interest per year  

Now, the function can be rewritten to identify the monthly interest rate is;

$A = P(1+\frac{0.023}{12})^{12t}$

here, n =12 ;

For monthly rate of interest =  $\frac{r}{12}$ = $\frac{0.023}{12} =0.0019$(approx) or 0.19% .

Therefore, the approximate monthly rate of interest is, 0.19%

Answer 2

The function is A=1000(1.023 1/2)^12t
and the interest is 0.19%

I hope this helps