5.12 Lump Sum Payments and Refinancing Mortgages
Learning Outcomes
Calculate the extra amount borrowed when refinancing a mortgage or the reduced payment size when renewing a mortgage and making a lump sum payment that drops the balance owing.
It is possible to borrow more money or pay off part of your mortgage when you go to renew your mortgage[1]. Let us first examine making a lump sum payment upon renewal (ie: making an additional payment when renewing your mortgage).
Lump Sum Payments
After a mortgage term is up and before a borrower renews their mortgage, they can choose to pay down some of the balance owing with a lump sum payment. This is like the initial down payment but part-way through the mortgage. It is often advisable to make these payments, if you can afford them, as they will save you a lot of interest if there are many years left in your mortgage.
Example 5.12.1
The Frasers term is up on their mortgage. They owe $523,324.15 on their at the end of the term. They have $125,000 saved up to pay down on their mortgage before they renew the mortgage. They will renew for another 15 years. They negotiate an interest rate of 2.88%, compounded semi-annually. What is the size of their new monthly mortgage payments?
First, let us determine the amount they will borrow (PV):
[latex]\text{New PV} = $523,324.15 - $125,000 = $398,324.15[/latex]
Next, let’s input the all values into the BAII Plus and calculate the size of their payments (PMT):
| B/E | P/Y | C/Y | N | I/Y | PV | PMT | FV |
|---|---|---|---|---|---|---|---|
| END | 12 | 2 | 15×12=180 | 2.88 | +398,324,15 | CPT −2,724.56 | 0 |
The Frasers will pay $2,724.56 per month on their mortgage.
Increasing the Size of a Mortgage Upon Renewal (Refinancing)
After a mortgage term is up, a borrower can choose to increase the size of their new mortgage[2] by borrowing additional money against the mortgage when they renew. Unless necessary, it is often not advisable to increase the size a mortgage. This is because a borrower will pay a lot of interest on the extra money borrowed if there are many years left on the mortgage.
Example 5.12.2
Craig and Joel’s mortgage term is up. For the last 5 years, their mortgage payments have been $3,904/month. Interest rates have dropped since they first bought their place. They are hoping to borrow some money to renovate their kitchen while still keeping their mortgage payments the same (at $3,904/month). How much can they borrow to renovate if they owe $523,324.15 and have 15 years left on their mortgage? Their new interest rate will be 1.99%, compounded semi-annually.
If we want to know how much Craig and Joel can borrow, we need to calculate the PV (amount owed) using the $3,904 payment and using the 15 years remaining to calculate N:
| B/E | P/Y | C/Y | N | I/Y | PV | PMT | FV |
|---|---|---|---|---|---|---|---|
| END | 12 | 2 | 15×12=180 | 1.99 | CPT +607,464.81 | −3,904 | 0 |
Take the difference between the amount they can borrow (PV) and the original amount they would have owed to determine how much extra Craig and Joel can borrow:
[latex]\textrm{Extra Amount Borrowed} = \$607,464.81 – \$523,324.15 = \$84,140.66[/latex]
Conclusion: Craig and Joel can borrow $84,140.66 to renovate their kitchen[3].
Your Own Notes
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The Footnotes
- If you borrow more money when your mortgage term is up, this is called refinancing (instead of renewing). ↵
- Up to 80% of the value of the house can be financed (borrowed). ↵
- Provided that the new value of their mortgage does not exceed 80% of the assessed value of their house. Their house would need to worth at least $759,331.02 for the bank to lend them up to $84,140.66 for their renovation. ↵
