what is the approximate monthly interest rate? drag and drop the choices into the boxes to correctly…

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. (select only 1 function and only one daily growth rate) function monthly interest rate $a = 1000(1 + 0.023)^{12t}$ $a = 1000(1.023^{\frac{1}{12}})^{12t}$ $a = 1000(1.023^{12})^{\frac{t}{12}}$ 0.19% 0.23% 0.31%

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. (select only 1 function and only one daily growth rate) function monthly interest rate $a = 1000(1 + 0.023)^{12t}$ $a = 1000(1.023^{\frac{1}{12}})^{12t}$ $a = 1000(1.023^{12})^{\frac{t}{12}}$ 0.19% 0.23% 0.31%

Answer

Explanation:

Step1: Recall compound - interest formula

The general compound - interest formula is $A = P(1 + r)^n$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the interest rate per period, and $n$ is the number of periods. If we assume an annual interest rate $R$ and we want to find the monthly interest rate $r_m$, and the number of months in $t$ years is $n = 12t$. If the annual growth factor is $1 + R$, then for monthly compounding, $(1 + R)=(1 + r_m)^{12}$.

Step2: Analyze the first function $A = 1000(1 + 0.023)^{12t}$

Here, the annual growth factor is $1+0.023$. Let the monthly interest rate be $r_m$. Then $(1 + 0.023)=(1 + r_m)^{12}$. Solving for $r_m$, we have $1 + r_m=(1 + 0.023)^{\frac{1}{12}}$. Using a calculator, $(1 + 0.023)^{\frac{1}{12}}\approx1+0.0019$. So $r_m\approx0.19%$.

Answer:

Function: $A = 1000(1 + 0.023)^{12t}$, Monthly Interest Rate: $0.19%$