) You pay 20% down on a home with a purchase price of $150,000. The bank will loan you the remaining balance at 6.84% APR. You have an option to make annual payments with a 20-year payment schedule
What is the annuity payment under the annual plan? Is this a better deal than an option to make a monthly plan of payments? Explain in terms of the effective cost of borrowing.
What will be an ideal response?
Answer: The bank will loan you (1 - 0.2) × $150,000 = $120,000, and this is the PV.
The PVIFA using r = 6.84% and n = 20 is 10.727045.
The annual annuity payment is: PMT = = = $11,186.68.
This is a better deal than monthly payments because whenever you have to make payments more frequently, your effective cost of borrowing goes up. For example, using the EAR formula with C/Y = 12 and monthly rate = = 0.5700%, we get 7.0586%. Since the EAR is the same as the APR for annual payments, the effective cost of borrowing for annual payments is 6.84%, which is lower than 7.0586%.
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