Question

1. Suppose that you buy new furniture that costs $5,200, but you need to take out a loan. The furniture store can give you a loan. Suppose you take out a 24-month loan with a 8.25% add-on rate per year.

   (a) What are your monthly payments?
   (b) What is the total interest you will pay after you have finished paying off your

   loan?
   (c) What will your balance be after you have made 12 payments?

2. Suppose you bought a house and you borrowed $355,000 for 360 months at a fixed 0.302% monthly interest rate (you have an actuarial loan).

   1. (a) What is your initial loan payment?

   2. (b) After 159 months (and therefore 159 payments), how many payments

      remain?

   3. (c) After 159 payments, what is your loan balance?

   4. (d) After 159 payments, by how much has your initial loan balance fallen?

   5. (e) After 159 payments, how much interest have you paid so far?

3. Suppose that you buy new kitchen appliances (i.e. equipment) for your home that costs a total of $3,600 but you need to have a loan. The store can give you a loan. You take out a 18-month loan with a 6.25% discount per year.

   (a) What are your monthly payments?
   (b) How much do you still owe after 12 payments?
   (c) What is the total interest you will pay after you have finished paying off your loan?

4. Suppose you wish to buy a house and you borrow $340,000 for 360 months at a 0.406% monthly interest rate with an actuarial loan.

   (a) What your monthly payment?
   (b) What is the total interest you pay if you make all 360 payments over the

   30-year period?

5. Suppose you wish to buy a car and the most you can pay is $400 a month.

   (a) If you take a 72-month loan, your monthly interest rate is 0.75%. What is the most you can pay to buy a new car?

   (b) If you take a 48-month loan, your monthly interest rate is 0.50%. What is the most you can pay to buy a new car?

Answer 1

Ans. Cost of furniture, C = $5200

Annual interest rate, r = 8.25%

Monthly interest rate, i = r/12 = 0.6875%

Number of months, n = 24 months

Using the formula for present value of the equivalent cash flows we get,

C = EMI * [ (1 - 1/(1+0.006875)24)/ 0.006875)

=> EMI = 5200*0.6875/( 1 - (1+0.006875)24)

=> EMI = $235.775

b) Month. Interest paid Principal left

0    0 5200

1 35.75 5164.75

2 35.50 5129.25

3 35.26 5094

4 35 5060

5 34.80 5025.20

6 34.55 4990.65

7 34.31 4956.34

8 34.07 4922.26

9 33.84 4888.42

10 33.61 4855

11 33.38 4821.62

12 33.15 4788.5

Thus, Principal left after 1 year is $4788.5

c) Total interest paid = Total payment made - Loan

=> Total Interest paid = 24*235.775 - 5200 = $458.60

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