Author Question: You pay 10 down on a home with a purchase price of 280,000. Your bank will loan the remaining ... (Read 58 times)

rosent76 · **on:** Jul 10, 2018

You pay 10 down on a home with a purchase price of 280,000. Your bank will loan the remaining balance of 252,000 at 8.23 APR. You have an option to make annual payments or monthly payments on the loan.

Both options have a 30-year payment schedule. What are the annuity payments under the annual plan? What are the annuity payments under the monthly plan? In terms of the total cash outflows and the effective cost of borrowing, briefly compare both plans.
What will be an ideal response?

Question 2

You are offered a perpetuity that will pay you 18,000 per year starting in one year. The seller wants you to pay 300,000 for the perpetuity. If you buy it at that price, what return will you earn?

A) 6
B) 5
C) 7
D) 8
E) 9

Danny Ewald · **Reply #1 on:** Jul 10, 2018

Answer to Question 1

Answer: You will borrow (1 - 0.1) 280,000 = 252,000 and this is the PV. For the annual plan, the PVIFA using r = 8.23 and n = 30 periods is 11.01782.
The annual annuity payment is: PMT = = = 22,872.03.
The PVIFA using = 0.68583 and n = 30 12 = 360 periods is 133.35804. The monthly annuity payment is: PMT = = = 1,889.65.
Multiplying this payment by 12 gives 22,675.80. This total for 12 months (or one year) is less than the annual payment of 22,872.03. Thus, by increasing the number of payments per year, you reduce your total cash outflows. Using the EAR formula, we get an effective cost of 8.55 for the monthly plan. Since the effective cost is the same as the 8.23 APR, the effective cost under the annual plan is 8.23. Thus, under the monthly plan you decrease you cash outflows but increase your effective cost of borrowing.

Answer to Question 2

A