Question

Calvin borrows $20,000 from a car dealership to purchase a vehicle. The car dealership charges 12% interest, compounded monthly. Calvin is expected to pay off the loan principal and all interest charged with equal monthly payments over a 3-year period.

a. What will Calvin’s monthly payment need to be? (4 points)

b. With the first monthly payment, how much of this payment will be “interest”, and how much of this payment will be “principal”? (4 points)

c. Once the loan is completely paid off at the end of 3 years, what total amount of interest will Calvin have paid over the life of the loan? (4 points)

d. If, after making monthly payments (calculated in part (a)) for some time, Calvin decides to pay off the loan balance in full. He wants to pay the remaining loan balance along with his 18th payment. How much must Calvin pay at the end of the 18th month? (4 points)

E. Suppose that Calvin is not able to make his 5th monthly payment. To make up for this, the dealership allowed him to extend the loan period by 1 month. How much must this last payment be in order to repay the loan in full (at the end of month 37)? (4 points)

F. What would Calvin’s monthly payment have been if the dealership charged 6% APR, but still required monthly payments? Note: This is considering that Calvin made every monthly payment from the original 3-year loan period. (EC 5 Points)

I need E and F please I have the rest

Answer 1

Solution:

(e)

From the above schedule , If Calvin cannot pay the 5 th instalment

then amount outstanding at the end of 5 instalment = 18114.51 + 1 month interest

= 18114.51 + 18114.51 * 0.01

= 18114.51 + 181.14

= $18295.65

Now the $18295.65 amount to be paid in 36-4 = 32 instalment

Then, monthly payment =

= 182.9565 x 1.3749

0.3749

= $670.97

At the end of month 37 , Calvin will make payment of $670.97

Payment schedule is shown below:

(f)

Since no fees mentioned so it is assumed APR is the interest rate

Then r = monthly rate of interest = 6/100 x 1/12 = 0.005

Then monthly payment =

20000 x 0.005 x ( 1+0.005 ) ^ 36

= 100 x ( 1.005 ) ^ 36

=100 x 1.1967

0.1967

= $608.38 (upto 2 places of decimal)

So , if APR is 6% then monthly payment will be $608.38.

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