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}=(P((APR)/(n)))/(\lbrack1-(1+(R)/(n))^(-nt)\rbrack)`
`\text{PMT}=(20000((0.0875)/(12)))/(\lbrack1-(1+(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*24-20000`
`=\text{ \$}1900`

In Second Instance:

`\text{Amount paid (A)=P(1+}(r)/(n))^(nt)`
`A=20000(1+(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