RatedrillMonths to recover refinancing costs
A time value of money problem from Ratedrill. Solve it with one answer box, with fresh numbers on every attempt and the formula, calculator keystrokes and Excel version in the worked answer, and it is checked the moment you submit.
The task
You owe $120,000 on a mortgage at 6% APR with 300 monthly payments left. A lender offers to refinance the same balance at 3.5% APR over the same 300 months, for $5,750 in closing costs paid up front. Using both payments rounded to the cent, how many months of payment savings does it take to recover the closing costs? Give the answer to 2 decimals.
What this problem teaches
The formula: Months = closing costs / (old PMT - new PMT). That is about 2.8 years. Refinancing only pays if you keep the loan longer than that.
A hint if you get stuck
Compute the old and the new monthly payment, subtract to get the monthly saving, then divide the closing costs by it.
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