I do like to think about math occasionally, especially as I am often flummoxed by how little younger generations understand about math. Today, I’d like to tackle to idea of the 30-year mortgage amortization, versus a 25-year amortization. Let’s jump straight into the math. To make it simple, let’s say we get a $500,000 mortgage. The number doesn’t really matter as much as the amount of interest it will cost to pay back the mortgage. Let’s choose a 5% interest rate, with a 5-year term. Now in some countries it is possible to get a very long, for example in the US, you can get a 30-year fixed term, which means if it’s 5%, it’s 5% for 30 years, regardless of what the rates do. Not so much in Canada, but let’s assume it’s a perfect world, and the amortization involves a series of 5-year terms all at 5%. Below are two tables showing estimated calculations for 25 and 30 year amortization periods.
| Term 1 | Term 2 | Term 3 | Term 4 | Term 5 | TOTAL | |
|---|---|---|---|---|---|---|
| outstanding balance | $500,000 | $442,537.54 | $368,980.71 | $274,821.77 | $154,290.37 | |
| principal | $57,462.46 | $73,556.83 | $94,158.94 | $120,531.40 | $154,290.37 | $500,000 |
| interest | $117,019.04 | $100,924.67 | $80,322.55 | $53,950.10 | $20,191.11 | $372,407.47 |
| total | $174,481.50 | $174,481.50 | $174,481.49 | $174,481.50 | $174,481.48 | $872,407.47 |
| Term 1 | Term 2 | Term 3 | Term 4 | Term 5 | Term 6 | TOTAL | |
|---|---|---|---|---|---|---|---|
| outstanding balance | $500,000 | $458,808.56 | $406.080.02 | $338,583.04 | $252,181.18 | $141,579.50 | |
| principal | $41,191.44 | $52,728.54 | $67,496.98 | $86,401.86 | $110,601.68 | $141,579.50 | $500,000 |
| interest | $118,915.76 | $107,378.66 | $92,610.22 | $73,705.35 | $49,505.54 | $18,527.71 | $460,643.24 |
| total | $160,107.20 | $160,107.20 | $160,107.20 | $160,107.21 | $160,107.22 | $160,107.21 | $960,643.24 |
Does a 30-year mortgage help out? Yes, in terms of monthly payments, these are reduced, meaning on a yearly basis about $14,374 less will need to be spent, however the additional 5-years will add more interest, so in the overall context, more will interest will have to be paid, to the tune of $88,235.77 in the case of the example. Now of course there are things that would invariably reduce the amount of interest paid over the life of the mortgage, including increased payment frequency, and lump-sum payments, but like so many things in life, there is no free lunch.
The Craft of Coding 