Question

Question 1 (1 point)

Garrett took out a 60-month bank loan of $22,000 at an interest rate of 7.99%. Garrett budgets to pay $700 per month towards the loan. Write
an equation that represents how much total interest Garrett will pay towards the remaining balance of the loan at the end of each year. Let m
equal the number of months paid and requal the interest charged on the remaining balance.

Answer 1

The description for the problem is listed throughout the section below on explanations.

Explanation:

The given values are:

The amount of bank loan = $22,000

Interest rate = 7.99%

Pays monthly = $700

So, the principal amount decreases by 700 per month.

Now,

The principal amount at the end of the
`m^(th)` month = (22000 - 700 m)

Then,

The interest paid at the end of 1 year:

⇒
`(22000)0.0799+(22000-700)0.0799+...+(22000-700(11))0.0799`

On simplifying the above equation, we get

⇒
`0.0799[12(22000)-(11* 12)/(2)* 700]`

⇒
`0.0799[264000-11* 6* 700]`

⇒
`0.0799[264000-46200]`

⇒ $
`17402.22`

Therefore interest could be measured correctly at the end of each year, likewise.

⇒
`(2200-700m)R+(22000-700(m+1))R+...+(22000-700(m+11))R`

⇒
`R[12* 22000-700[12m+(11* 12)/(2)]]`

⇒
`R[264000-700[12m+(11* 12)/(2)]]`

⇒
`R[263300(12m+66)]`

R : interest rate