Question

Consider a 30-year, $115,000 fixed-rate mortgage with a nominal annual rate of 4.85 percent. All payments are made at the end of each month. What is the remaining balance on the mortgage after 5 years?

Answer 1

PV = 115,000
Rate per month = 4.85%/12
Number of Periods = 360
Remaining balance after 5*12 = 60 months
The monthly payments = PV/(1-(1+r)^-n)/r = 115,000/(1-(1+4.85%/12)^-360)/(4.85%/12) = 606.8456

For n = 60 months
The remaining balance after 5 years =  the future value of PV - Future value of annuity = PV*(1+r)ⁿ -PMT*(1+r)ⁿ-1)/r
= 115,000*(1+4.85%/12)⁶⁰ - 606.85*(1+4.85%/12)⁶⁰-1)/(4.85%/12) = 105,376.35

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