Question

Payment

Number
4. Monty Ricker obtained a
used car loan of $6,000.00
at 8% for 36 months. The
monthly payment is $187.80.
The balance of the loan after
12 payments is $4,159.90.
The balance after the 34th
payment is $380.60.
a. What is the interest for
the first payment?
b. What is the interest for the 13th payment?
c. Explain why the interest is so much different for the
1
2
3
4
5
6
Payment
$414.00
414.00
414.00
414.00
414.00
Balance
Amount for Amount for
Interest Principal $2,400.00
$390.00 $2,010.00
two payments.
d. What is the balance after the 35th payment?
$24.00
20.10

Answer 1

The solution is,

a) Current month's interest is: $40

b) The final payment is $7,440

c) Amount saved by paying off loan early is: $600

What is interest?

Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.

here, we have,

Principal = $6,000

Interest rate = 8% or 0.08

Time = 36 months or 3 years

After 20 payments, the payment is $2,849.08.

a) What is the CURRENT month's interest?

The formula used to find the interest is:

`I = P* r* t`

Where P = Principal Amount

r = interest rate

and t = time in years

Putting the given values:

`I = 6,000 * 0.08 * 3`

`I = 1440`

Total Interest = $1440

Current Month interest = 1440/36

Current Month interest = 40

So, Current month's interest is: $40

b) What is the final payment?

The formula used is:

`A = P(1+r* t)`

`A = 6,000(1+0.08*3)`

`A = 6000*(1.24)`

`A = 7,440`

So, the final payment is $7,440

c) How much is saved by paying off the loan early?

The current balance paid is $2,849.08

The loan is paid when next payment is due.

So, remaining amount to be paid is:

Remaining Amount = Final Payment - Current balance paid

Remaining Amount = 7,440 - 2,849.08

Remaining Amount = 4,590.92

Remaining months in which amount is to be paid: 36 - 20 = 16 months

The loan is paid off next month so interest rate of remaining 15 months = 15 x 40 = 600

The amount paid on next payment = 4590.92 - 600 = $3990.9

So, amount saved by paying off loan early is: $600