{"id":940,"date":"2020-08-10T14:23:34","date_gmt":"2020-08-10T18:23:34","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=940"},"modified":"2021-07-09T12:36:37","modified_gmt":"2021-07-09T16:36:37","slug":"refinancing","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/refinancing\/","title":{"raw":"5.12 Lump Sum Payments and Refinancing Mortgages","rendered":"5.12 Lump Sum Payments and Refinancing Mortgages"},"content":{"raw":"
\r\n

Learning Outcomes<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nCalculate 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.\r\n\r\n<\/div>\r\n<\/div>\r\nIt is possible to borrow more money or pay off part of your mortgage when you go to renew your mortgage[footnote]If you borrow more money when your mortgage term is up, this is called refinancing (instead of renewing).[\/footnote]. Let us first examine making a lump sum payment upon renewal (ie: making an additional payment when renewing your mortgage).\r\n

Lump Sum Payments<\/h1>\r\nAfter 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<\/strong>.\u00a0 This is like the initial down payment but part-way through the mortgage.\u00a0 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.\r\n

Example 5.12.1<\/h2>\r\nThe Frasers term is up on their mortgage.\u00a0 They owe $523,324.15 on their at the end of the term.\u00a0 They have $125,000 saved up to pay down on their mortgage before they renew the mortgage.\u00a0 They will renew for another 15 years.\u00a0 They negotiate an interest rate of 2.88%, compounded semi-annually.\u00a0 What is the size of their new monthly mortgage payments?\r\n\r\nFirst, let us determine the amount they will borrow (PV):\r\n

[latex]\\text{New PV} = $523,324.15 - $125,000 = $398,324.15[\/latex]<\/p>\r\nNext, let's input the all values into the BAII Plus and calculate the size of their payments (PMT):\r\n\r\n\r\n\r\n\r\n\r\n
B\/E<\/th>\r\nP\/Y<\/th>\r\nC\/Y<\/th>\r\nN<\/th>\r\nI\/Y<\/th>\r\nPV<\/th>\r\nPMT<\/th>\r\nFV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
END<\/td>\r\n12<\/td>\r\n2<\/td>\r\n15\u00d712=180<\/td>\r\n2.88<\/td>\r\n+398,324,15<\/td>\r\nCPT<\/span><\/strong> \u22122,724.56<\/span><\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe Frasers will pay $2,724.56 per month on their mortgage.\r\n\r\n \r\n

Increasing the Size of a Mortgage Upon Renewal (Refinancing)<\/h1>\r\nAfter a mortgage term is up, a borrower can choose to increase the size of their new mortgage[footnote]Up to 80% of the value of the house can be financed (borrowed).[\/footnote] by borrowing additional money against the mortgage when they renew.\u00a0 Unless necessary, it is often not advisable to increase the size a mortgage.\u00a0 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.\r\n

Example 5.12.2<\/h2>\r\nCraig and Joel's mortgage term is up. For the last 5 years, their mortgage payments have been $3,904\/month.\u00a0 Interest rates have dropped since they first bought their place.\u00a0 They are hoping to borrow some money to renovate their kitchen while still keeping their mortgage payments the same (at $3,904\/month).\u00a0 How much can they borrow to renovate if they owe $523,324.15 and have 15 years left on their mortgage?\u00a0 Their new interest rate will be 1.99%, compounded semi-annually.\r\n\r\nIf 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:\r\n\r\n\r\n\r\n\r\n\r\n
B\/E<\/th>\r\nP\/Y<\/th>\r\nC\/Y<\/th>\r\nN<\/th>\r\nI\/Y<\/th>\r\nPV<\/th>\r\nPMT<\/th>\r\nFV<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
END<\/td>\r\n12<\/td>\r\n2<\/td>\r\n15\u00d712=180<\/td>\r\n1.99<\/td>\r\nCPT<\/strong> +607,464.81<\/td>\r\n\u22123,904<\/span><\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTake 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:\r\n\r\n[latex] \\textrm{Extra Amount Borrowed} = \\$607,464.81 \u2013 \\$523,324.15 = \\$84,140.66 [\/latex]\r\n\r\nConclusion: Craig and Joel can borrow $84,140.66 to renovate their kitchen[footnote]Provided that the new value of their mortgage does not exceed 80% of the assessed value of their house.\u00a0 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.[\/footnote].\r\n

Your Own Notes<\/h1>\r\n