THE SCENARIO
John and Jane Smith want to retire in 12 years, they currently have $250,000 invested in a bond fund earning 2.8%, and they need $875,000 to retire. They owe $97,500 on their current mortgage (7% borrowing rate, set to be paid off in 12 years), and are considering refinancing their house, borrowing $186,044.55 for 15 years at 3.5%.
THE QUESTION
If they pay off their current mortgage and take out this 15 year mortgage(assume no closing costs),
A) How much money will they have left over after refinancing their house and paying off the old mortgage?
B)Investing the surplus from the refinance in addition to their current $250,000, what yield do they need to getover the next 12 years to get to their new goal amount of$920,389.27?
C) If they invested an additional $250 per month, what yield would they need to reach their new goal amount of$920,389.27?
THE SOLUTION
A)How much money will they have left over after refinancing their house and paying off the old mortgage?
Current loan balance = $97,500
Borrowed amount = $186,044.55
Difference =$186,044.55 - $97,500 =$88,544.55
After paying off their balance, they will have $88,544.55 additional to invest.
B)Investing the surplus from the refinance in addition to their current $250,000, what yield do they need to getover the next 12 years to get to their new goal amount of$920,389.27?
N = 144
PV = $250,000 + $88,544.55 = $338,544.55
PMT = $0
FV = -$920,389.27
I/YR = 8.36%
So by trading 7% debt for 3.5% debt and investing the extra money they were able to borrow, they only need to get an 8.36% yield.
C)If they invested an additional $250 per month, what yield would they need to reach their new goal amount of$920,389.27?
N = 144
PV = $250,000 + $88,544.55 = $338,544.55
PMT = $250
FV = -$920,389.27
I/YR = 7.80%
So by trading 7% debt for 3.5% debt and investing the extra money they were able to borrow, and making the commitment to invest an additional $250 per month, they only need to get an 7.80% yield.
