Question

Suppose you buy a fridge for $1580. You agree to pay off the total amount with monthly payments over 2 years at j12= 11%. If you wish to refinance you will have to pay a penalty equal to 4 months' interest on the outstanding balance. After 12 payments you see that interest rates at your bank are j12j = 6.5%.

(a) Calculate the original monthly payment.

Answer: $

(b) Calculate the new monthly payment if you were to refinance under your banks interest rate. (Assume the original term does not change.)

Answer: $

(c) Should you refinance?

Answer:   ?    yes    no   

NOTE: When calculating a payment or outstanding balance, round appropriately and carry that value through further calculations.

Answer 1

Answer (a)

original monthly payment   

r*(PV) 1-(1+r)-n

Here, r = interest rate (Monthly) = 11% / 12 = 0.009583

PV = Present Value of Bprrowing =  $1580

n = Payback Periord (No of Installments) = 24 Months

So, monthly payment    

10.009167 + 1580 1-(1+0.009167)-24 14.4838 1-1.009167-24 14.4838 1-0.8033

Answer (b)

Interest Rate = 11%
Monthly Rate = 11% /12 = 0.009166667
Starting Balance = 1580

Months	Interest	Monthly Payment	Principal Payment	Balance Amount
1	14.48	73.64	59.16	1520.84
2	13.941064	73.64	59.70	1461.14
3	13.393824	73.64	60.25	1400.90
4	12.841567	73.64	60.80	1340.10
5	12.284248	73.64	61.36	1278.74
6	11.72182	73.64	61.92	1216.83
7	11.154237	73.64	62.49	1154.34
8	10.581451	73.64	63.06	1091.28
9	10.003414	73.64	63.64	1027.64
10	9.4200788	73.64	64.22	963.43
11	8.8313962	73.64	64.81	898.62
12	8.2373173	73.64	65.40	833.21

Here,

Interest = Monthly Interest Rate * Balance Amount

For 01st Month = 1580 * 0.009166667 = 14.48

For 02nd Month = 1520.84 * 0.009166667 = 13.94

Principal Payment = Monthly Payment - Interest Pay

Now after 12 Months priciple outstanding will be $ 833.21.

To refinance loan Needs to pay 04 Months Interest on upfront = 04*Monthly Interest Rate * Balance Amount

= 04*0.009166667*833.21.= 30.55

So Refinance Loan will be = 30.55 + 833.21 = 863.76

Now,

Tenure of loan n = 12 Months

r = interest rate (Monthly) =6.5% / 12 = 0.005417

PV = $ 863.76

Monthly Payment will be,

| 0.005417 + 863.76 1-(1+0.005417-12 4.6789 1-1.005417-12 4.6789 0.9372 1

Answer(c)

Should You Refinance : No Here Monthly repayment goes higher as compared to previous monthly payment of $73.64