Prob 45 Please assist with E 5 3 points Current 30year mortg

Prob 4.5 Please assist with (E)

5. (3 points) Current 30-year mortgages are available as follows:

Option A: 4.625% (0 points)

Option B: 4.25% (2.0 points).

a. For a $200,000 mortgage calculate the monthly payments for each mortgage program, quoted to 2 decimal places, e.g. $832.58.

b. Using the cost-benefit approach in Example 7-4 on p. 225 over a 30-year period, which option do you recommend? Explain why in an essay. Time value of money calculation, and explanation required.

b. Since we are going to keep the mortgage loan for 30 years, ofcourse less the interest rate, more the cost benefi. hence one should go with option B i.e 4.25%

c. If you plan to live in the house for only 4 years, which mortgage would you recommend and why? Time value of money calculation and explanation in an essay are required. Hint: Compare the PV of the monthly savings to the cost of the points.

.c. if one is going to live only for 4 years, less the EMI more the benefit. Hence going with option B will be more beneficial hence, less will be the EMI more will be the montlhy savings.

d. If you plan to live in the house for 12 years, which mortgage would your recommend and why? Time value of money calculation and explanation in an essay are required. Hint: Compare the PV of the monthly savings to the cost of the points.

d. In long term also, less the interest rate, more the benefit hence, one should go with 4.25%

e. Calculate the breakeven number of months you would have to live in the house to make you indifferent between the two mortgages. Explain your answer in a full essay.

E) Please calculate this

Solution

Answering the specific point (e) which is asked for, by you.

Monthly Mortgage payment is given by formula : Loan Amount * [r * (1+r)^t] / [(1+r)^t - 1] ; where r is the applicable monthly interesr rate (annual rate / 12) and t is time period in months.

In this case for $200000. the monthly mortgage payment shall be :

a. Interest rate = 4.625% or 0.39%:

Monthly Payment = 200000 * [0.39% * (1+0.39%)³⁶⁰]/[(1+0.39%)³⁶⁰ - 1] = 1028.28

b. Interest rate = 4.25% or 0.35%:

Monthly Payment = 200000 * [0.35% * (1+0.35%)³⁶⁰]/[(1+0.35%)³⁶⁰ - 1] = 983.88

Now the monthly benefit = (1028.28 - 983.88) = $44.40

Upfront cost for this benefit is = 2 points or 2% which is 200000 * 2% = $ 4000

So this monthly benefit is like an annuity stream. The break even point will be the time t in months at which point the present value of this annuity stream will equal 4000 (upfront cost) at the discount rate which is the difference in the interest rates i.e. (4.625%-4.25%)/12 - divide by 12 to make it monthly interest rate.

PV of annuity is given by : PV = Periodic Cash flow * [1-(1+r)^-t] / r ; where r is the discount rate and t is the time in months. Plugging in the values:

4000 = 44.4 * [1 - (1+0.031%)^-t] / 0.031% ; solving for t, we get t = 91.39 months. Hence the breakeven point will be 91.39 months