Question

 

Aisling and Andrew are looking to purchase a doomsday bunker where they plan to live full time until a vaccine for Covid-19 is available. For the past six years they have been able to put $400 every month into a savings account with an APR of 1.05%.

a. (20 pts) How much do Aisling and Andrew have saved toward a down payment?

Aisling and Andrew qualify for a 30-year mortgage with a 3.95% APR or a 15-year mortgage with a 2.85% APR. They found a contractor that can install and equip a full amenity 1600 sq ft. bunker in their backyard for $315,000. Aisling and Andrew believe they can afford a monthly payment of $1,800 toward the purchase of this bunker.

b. (20 pts) Assuming Aisling and Andrew will make payments for the entire life of the loan, how much would they pay in total for each loan option (including the down payment)?

Andrew has been working with his Uncle Al over the past few years flipping investment properties in Flagstaff. This has been a very profitable endeavor for Al. As a thank you for all of Andrew’s hard work, Al decided to gift Aisling and Andrew $10,000 toward the purchase of the bunker.

c. (20 pts) If Aisling and Andrew decide to put Uncle Al’s gift toward their down payment, how will this affect the total amount they would pay over the life of the loan for each loan option?

It is right around the same time Uncle Al makes his offer that Aisling and Andrew’s loan officer informed them about mortgage points. Mortgage points, also referred to as discount points, are a way to pay in advance to reduce your interest rate. “Buying down the rate” by using mortgage points can lower your monthly mortgage payment and help you save interest over the life of the loan. In general, people can expect to lower the interest rate of their loan by 0.25% for every 1% of the loan amount they pay when closing on their bunker. For example, if a couple needed to borrow $250,000 to purchase a bunker and were offered a 5.25% APR, they could reduce their interest rate from a 5.15% APR to a 5% APR by purchasing one point for $2500 at their closing.

d. (20 pts) Aisling suggests they use some of Uncle Al’s gift toward purchasing a point (or two) instead of using it all toward a down payment. If Aisling and Andrew decide to pay to reduce their interest rate, how will this affect the total amount they would pay over the life of the loan for each loan option (don’t forget to factor in the original down payment amount)?

e. (20 pts) Calculating and stating any other quantities you believe are important, make and justify a recommendation for Aisling and Andrew regarding the purchase of this bunker. Address any features you believe are significant. For example, which options allow them to stay within their budget? Which loan offer from their bank should they pursue? Should they purchase mortgage points? Is this bunker a worthwhile expense?

Answer 1

(a) Calculation of amount of savings

Savings per month = $400

APR = 1.05%

Period = 6 years i.e. 72 months

Monthly Interest rate = 1.05 / 12 = 0.0875%

So, Amount accumulated for payment of downpayment at the end of 6 years is

FVIFA(0.0875%,72 months) * 400 = 74.3479 * 400 = $ 29739.14

Therefore, the amount of savings is $ 29,739.14

(b)

Assuming that $ 315,000 includes the cost bunker.

Amount of loan required = $ 315,000 - $ 29739.14 = $ 285260.85

If 30 year mortgage with 3.95% APR is chosen

-> Monthly interest rate = 3.95 /12 = 0.3292%

-> Period = 30 years *12 =            360 months

-> Monthly payment to be done = $ 285260.85 / PVIFA ( 0.3292%, 360 months)

= $ 285260.85 / 210.7214 = $ 1353.73 per month

-> Total payment = ($ 1353.73 * 360 months) + $ 29739.14 = $ 487344.40 + $ 29739.14 = $ 517083.5

If 15 years mortgage with a 2.85% APR

-> Monthly interest rate = 2.85 / 12 = 0.2375%

-> Period = 15 years *12 = 180 months

-> Monthly payment to be done = $ 285260.85 / PVIFA ( 0.2375%, 180 months)

= $ 285260.85 / 146.3293 = $ 1949.45

-> Total payment = ($ 1949.45 * 180 months) + $ 29739.14 = $ 350,901 + $ 29739.14 = $ 380640.1

As Aisling and Andrew believe they can afford a monthly payment of $1,800 toward the purchase of this bunker, they would prefer 30 year loan.

(c)

If $ 10,000 received from Uncle Al is put down payment

The required amount for loan will be $ 315,000 - $ 29739.14 - $ 10,000 = $ 275,260.86

So, Monthly payment in case of 30 year loan

= $ 275,260.86 / PVIFA ( 0.3292%, 360 months)

= $ 275,260.86 / 210.7214

= $ 1306.28

And

Monthly payment in case of 15 year loan

= $ 275260.85 / PVIFA ( 0.2375%, 180 months)

= $ 275260.85 / 146.3293

= $ 1881.11

In the present scenario too, 15 year loan is out of their budgeted figure.

(d)

Loan requirement = $ 315,000 - $ 29739.14 = $ 285260.85

So, the price of 1 point is $ 285,260.85 * 1% = $2852

Maximum points that can be purchased = $ 10,000 / $ 2852 = 3.50 or 3

(it is assumed that they will purchase as much points as they can afford)

(it is also assumed that the amount remaining after purchase of points is not paid as down payment towards loan)

If the amount received as a gift is put into purchasing points

The APR will be reduced by 0.25% * 3 = 0.75%

=> So, the monthly payment for 30 year loan will be

APR = 3.95% - 0.75% = 3.20%

Monthly rate of interest = 3.20% / 12 = 0.2667%

Monthly payments to be done = $ 285260.85 / PVIFA ( 0.2667%, 360 months)

= 285,260.85 / 231.2199 = $ 1233.72

=> And, the monthly payment for 15 year loan will be

APR = 2.85% - 0.75% = 2.10%

Monthly rate of interest = 2.10% / 12 = 0.175%

Monthly payments to be done = $ 285260.85 / PVIFA ( 0.175%, 180 months)

= $ 285260.85 / 154.2915 = $ 1848.84

(e)

From above calculation, following can be interpreted

Option (i) Monthly payments if gift is utilised as down payment

30 year loan = $ 1306.28

15 year loan = $ 1881.11

Option (ii) Monthly payments if gift is utilised for purchasing Mortgage points

30 year loan = $ 1233.72

15 year loan = $ 1848.84

The instalment amount of 15 Year loan is out of budget in both the option.

The instalment amount of 30 Year loan is less in Option (ii), so they should purchase mortgage units and pursue with 30 Year loan.