Mathematics: Rufus took out a 2 year loan for 1500 at an electronics store to be paid back with monthly at a 14.4 apr compounded monthly if the loan offers no payments for the first 4 months how much will rufus owe when he begins making payment?

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Rufus took out a 2 year loan for 1500 at an electronics

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10.03.2022

$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.

$A=P(1+\frac{r}{n})^{nT}$ , 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.

$14.4\%=\frac{14.4}{100}=0.144$

$4\text{ months}=\frac{4}{12}\text{ year}$

Upon substituting our given values in compound interest formula we will get,

$A=1500(1+\frac{0.144}{12})^{12\times \frac{4}{12}}$

$A=1500(1+0.012)^{4}$

$A=1500(1.012)^{4}$

$A=1500\times 1.048870932736$

$A=1573.306399104\approx 1573.31$

Therefore, Rufus will owe $1573.31 when he begins making payment.

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