Your friend tells you he has a very simple trick for taking one-third off the ti
ID: 2612443 • Letter: Y
Question
Your friend tells you he has a very simple trick for taking one-third off the time it takes to repay your mortgage: Use your Christmas bonus to make an extra payment on January 1 of each year ( that is, pay your monthly payment due on that day twice). If you take out your mortgage on July 1, so your first monthly payment is due August 1, and you make an extra payment every January 1, how long (in years) will it take to pay off he mortgage? Assume that the mortgage has an original term of 30 years and an APR of 7.8%. (Hint: The original balance does not matter in this problem, so you can pick any number you want. In this case we will use $100,000 as the principal balance.) Round to three decimal places.
Explanation / Answer
Solution-
Calculation on Excel as follows...
Excel Formula
Interest rate
7.80%
Required monthly payment
719.87
=PMT(7.80/12,30*12,100,000)*-1
Extra payment
719.87
Number of months between extra payments
12
Months until extra payment begins
6
Original Term of Loan
30
Beginning loan value (assumed)
100000.00
Loan will be paid off at payment number
276.55
or about
23.5 Years
=276.55 /12
Excel Formula
Interest rate
7.80%
Required monthly payment
719.87
=PMT(7.80/12,30*12,100,000)*-1
Extra payment
719.87
Number of months between extra payments
12
Months until extra payment begins
6
Original Term of Loan
30
Beginning loan value (assumed)
100000.00
Loan will be paid off at payment number
276.55
or about
23.5 Years
=276.55 /12
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