Question 1 (mortgage problem) You purchase a house that costs $625,000 with an 8
ID: 2708509 • Letter: Q
Question
Question 1 (mortgage problem)
You purchase a house that costs $625,000 with an 8%, 30-year mortgage. You make a 20% down payment to avoid PMI insurance.
What is your monthly payment?
Amortize the first and second payments.
What is the mortgage balance after 5 years?
What percentage of the principal is paid off after 5 years?
Suppose after 5 years you refinance at 6% the remaining balance at a cost of
$10,000, for 30 years. What is your new monthly payment?
Further, suppose you maintain the same payments as in (1), i.e. pre-pay on the principal, how many YEARS until you payoff the mortgage?
Question 2 (2nd mortgage problem)
You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.
What is the monthly payment?
During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?
How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?
How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month
Explanation / Answer
You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.
What is the monthly payment?
During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?
How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?
How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current months principal?
The Price is $500,000
Down payment 20% or -$100,000
Present Value (Loan Balance)= $400,000
Term 30 years or 360 months
APR is 8% or 0.67% per month
monthly payment is: $2,935.06
You can use the Financial formulas in
=PMT(rate,npr, pv)
If you increase the principal payment by $300 per month or $3,235.06
The loan will be paid off in 261.7 months
=nper(rate, pmt,pv)
Based on these answers please try question #2 and 4 on your own.
HINT: Q 2. the monthly payments consist of principal payment plus interest.
1st Month: Interest payment is .6667% x $400,000 = $2,666.67
Principal payment is $2,935.06 - $2,666.67 = $268.39
So the Principal balance is $400,000 - $268.39=$399,731.61
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