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Question 1142424: Lily and Frank found a house they like, and to buy it they will have to borrow $360,000 from their bank at 6.575% per annum, repayable over 20 years
5 years after taking out their loan, Lily and Frank inherited $80,000 from a relative and decided to use it to help pay down their loan. After the payment was made, the bank offered two options
-Continue to pay off the loan with monthly repayments as previously calculated (and complete loan sooner)
Or
-Continue to pay off loan over 15 remaining years with monthly repayments
i) Which option will cost Lily and Frank the least money overall?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! original loan is for 360,000 at 6.575% per year compounded monthly.
using texas instruments business analyst 2, i make the following inputs.
present value = 360,000
future value = 0
number of time periods = 20 years * 12 months per year = 240
interest rate percent = 6.575% per year / 12 = .547916667 per month.
payments are made at the end of each month.
the calculator tells me that the monthly payment needs to be 2,699.982573.
the calculator tells me that the remaining balance at the end of the 60th month is 308,486.3443.
80,000 is deducted from this to get a remaining balance of 228,486.3444.
the inputs to the calculator are now.
present value = 228,486.3443
future value = 0
monthly interest rate is the same as originally determined.
monthly payment is the same as originally determined.
payments are made at the end of each month.
the calculator tells me that the number of months required to pay off the loan is 114.0174191.
that' considerable less than the 180 months that would have been required without deducting the 80,000.
that's the first option.
the second option is to calculate the payments again over a 180 month period (15 years) and complete the loan in the same amount of time as was originally determined.
the inputs to the calculator are now.
present value = 228,486.3443
future value = 0
monthly interest rate is the same as originally determined.
payments are made at the end of each month.
number of months are 180 (15 years * 12 = 180).
the calculator tells me that the new monthly payments need to be 1,999.794024.
with the first option, the sum of the monthly payments for 114.017419 months will be 2,699.982573 * 114.017419 = 307.845.0446.
with the second option, the sum of the monthly payments for 180 months will be 1,999.794024 * 180 = 359,962.9243.
looks like the first option is cheaper in terms of total money spent.
that would be the option of 2699 per month for 114 months.
i also used excel to do a month by month analysis and it told me the same story.
here's some snapshots of the excel analysis.
if you have any questions about any of this, send me an email (dtheophilis@gmail.com).
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