Answer:
$1573.31
Step-by-step explanation:
We have been given that an electronics store to be paid back with monthly at a 14.4 APR compounded monthly.
As Rufus will begin to make payments after 4 months, so we will find the total amount after 4 months using compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A = Final amount after T years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest in compounded per year,
T = Time in years.
Let us convert given interest rate in decimal form.
[tex]14.4\%=\frac{14.4}{100}=0.144[/tex]
[tex]4\text{ months}=\frac{4}{12}\text{ year}[/tex]
Upon substituting our given values in compound interest formula we will get,
[tex]A=1500(1+\frac{0.144}{12})^{12\times \frac{4}{12}}[/tex]
[tex]A=1500(1+0.012)^{4}[/tex]
[tex]A=1500(1.012)^{4}[/tex]
[tex]A=1500\times 1.048870932736[/tex]
[tex]A=1573.306399104\approx 1573.31[/tex]
Therefore, Rufus will owe $1573.31 when he begins making payment.
