Question

In one instance, a financial institution loaned you $20,000 for two years at an APR of 8.75% for which you must make monthly payments. In a second instance, you loaned a financial institution $20,000 for two years at an APR of 8.75% compounded monthly. What is the difference in the amount of interest paid? (Round your answer to the nearest cent.)

Answer 1

Given:

In one instance:

P=$20000 ; APR=8.75% ;t=2 years ; n=12 months

$\text{PMT}=\frac{P(\frac{APR}{n})}{\lbrack1-(1+\frac{R}{n})^{-nt}\rbrack}$$\text{PMT}=\frac{20000(\frac{0.0875}{12})}{\lbrack1-(1+\frac{0.0875}{12})^{-24}\rbrack}$$\text{PMT}=\frac{20000(0.0073)}{\lbrack1-0.84^{}\rbrack}$$\text{PMT}\approx\text{ \ 912.5}$

Interest paid :

$=912.5\times24-20000$$=\text{ \ }1900$

In Second Instance:

$\text{Amount paid (A)=P(1+}\frac{r}{n})^{nt}$$A=20000(1+\frac{0.0875}{12})^{24}$$A=20000(1.1905)$$A\approx\text{ \ 23810}$$\text{Interest paid =23810-20000}$$\text{Interest Paid= \ 3810}$

Difference in the amount of interest paid = 3810-1900

Difference in the amount of interest paid = $1910