**Question 759** time calculation, fully amortising loan, no explanation

**Five** years ago you entered into a **fully amortising** home loan with a principal of $**500,000**, an interest rate of **4.5**% pa compounding monthly with a term of **25** years.

Then interest rates suddenly fall to **3**% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.