MATH SOLVE

6 months ago

Q:
# 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?Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table.Function Monthly interest rateA = 1000(1 + 0.023)^12tA = 1000(1.023^12)^t/12A = 1000(1.023^t/12)^12t0.23%0.19%0.31%

Accepted Solution

A:

Answer:The total amount of money in a saving account after t years is given by:[tex]A = 1000(1.023)^t[/tex] we can write this function as; [tex]A = 1000(1+0.023)^t[/tex] .....[1]Use the formula:-[tex]A = P(1+\frac{r}{n})^{nt}[/tex] ; whereP = 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;[tex]A = P(1+\frac{0.023}{12})^{12t}[/tex]here, n =12 ;For monthly rate of interest = [tex]\frac{r}{12}[/tex] = [tex]\frac{0.023}{12} =0.0019[/tex](approx) or 0.19% .Therefore, the approximate monthly rate of interest is, 0.19%

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;[tex]A = P(1+\frac{0.023}{12})^{12t}[/tex]here, n =12 ;For monthly rate of interest = [tex]\frac{r}{12}[/tex] = [tex]\frac{0.023}{12} =0.0019[/tex](approx) or 0.19% .Therefore, the approximate monthly rate of interest is, 0.19%