Question 1138984: When applying for a mortgage, find one that allows you to contribute more money than the required monthly payment. The following problems illustrates why. Lets say that you have a 30-year $142,650 fixed rate mortgage at 4.51% interest compounded monthly. Instead of paying the regular monthly payment for the mortgage, you decide to add an additional $150 to each of your monthly payments. By paying the extra $150 a month, the extra amount in each payment is applied directly to reducing the principal. This means that (1) the length of the loan is reduced since the principal will be reduced faster (than if no extra amount was paid with your monthly payment) and (2) you eventually pay less in interest than if you were to pay the only regular monthly payment required.
a.) Find out how many years it will take you to pay off the loan if you were to pay the additional $150 with each monthly payment? Use TVM solver.
b.) How much money will you save in interest if you pay the additional $150 with each monthly payment than if you did not pay any additional amount each month?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not sure which tvm solver you are asked to use.
i use the texas instruments business analyst 2 plus (TI BA II Plus).
the first thing necessary to do is to find out what the regular payments are.
the inputs to the calbulator were:
pv = 142650
fv = 0
n = 30 * 12 = 360 monthly payments.
i/y (interest rate) = 4.51% per year / 12 = .375833333...% per month.
payments are set to be made at the end of the month.
i click on pmt and the calculator tells me that the monthly payments are $723.6344358.
the interest paid on this loan is 360 * the monthly payment minus the original balance on the loan = 723.6344358 * 360 - 142650 = $117.8583969.
i then added $150 to the original payment to make it $873.6344358 and entered that into the pmt field and then clicked on n (number of time periods).
the calculator tells me that the number of time periods is 253.532159.
the interest paid on this loan is 253.532159 * 253.532159 - 142650 = $78,844.42466.
the interest paid on the 360 month loan minus the interest paid on the 253.532159 month loan is equal to $39,013.97221.
i'm not sure how your TVM calculator does it, but there may be some difference due to rounding of intermediate results.
you should, however, be in the ball park.
most TVM calculators work the same way.
the procedure i used was as shown above.
first find the regular payment on a 360 month loan at the monthly interest rate.
then add the 150 to the regular payment.
then calculate the number of months to repay the loan at the same monthly interest rate with the new payments.
some online calculsators give you the payments rounded to the nearest penny.
that will make the numbers come out a little different.
if you can, send me the url for the online calculcator you are using so i can compare the results i get with that.
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