Assume that you are 10 years into a 30 year home loan at 5.3%. You owe $280,000
ID: 2374631 • Letter: A
Question
Assume that you are 10 years into a 30 year home loan at 5.3%. You owe $280,000 left on your home at this time. You can refinance your loan at 3.1% for 20 years; however the closing costs will be around $3,500.
a. If you go for refinancing, how many more months would you need to live in the home in order to get the closing cost back? Ignore time value of money and tax credits of the interest payments_______________
b. Answer part (a) again considering time value of money and MARR 10% compounded monthly. Ignore tax credits of interest again _______________
Explanation / Answer
(a) Current payment/month is calculated in Excel as =PMT(5.3%/12,240,-280000,0,0), where the first parameter is interest rate on monthly basis, 240 is no of months remaining on mortgage, and 280,000 is principal left to be paid. This is $1895/month. New payment/month is calculated as =PMT(3.1%/12,240,-280000,0,0), the only difference being the interest rate. This is $1567/month. The saving is 1895-1567 = $328/month. So the $3,500 closing costs can be recouped in 3500/328 = 10.67 months, or approximately 11 months. (b) Considering time value of money and average interest rate being 10%/12 per month, the Excel formula is =NPER(10%/12,-328,3500,0,0), i.e. the number of payments required of $328 to equal current value of $3500 at the rate of 10%/12 per month. This is 11.22 months, or approximately 12 months. Please ignore my formatting - am having some issues with my browser. Thanks and let me know in case of any queries.