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?
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.
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