Question

I have a choice between two different fixed-rate mortgages when I purchase my $150,000 house. One is a 20-year mortgage with a quoted rate of 4.375% and the other is a 30-year mortgage with a quoted rate of 4.5%. Both rates are monthly compounded, and both mortgages require equal monthly payments. What is the required monthly payment of each loan? How much of a down payment would I have to make if I wanted the 20-year loan’s payment to be that of the 30-year loan payment (with no down payment)?

Answer #1

Monthly payment in option 1 | Using pmt function in MS excel | pmt(rate,nper,pv,fv,type) rate = 4.375/12 =.364% nper = 12*20 =240 pv = 150000 fv =0 type =0 | PMT(0.3645%,240,150000,0,0) | ($938.80) |

Monthly payment in option 2 | Using pmt function in MS excel | pmt(rate,nper,pv,fv,type) rate = 4.5/12 =.375% nper = 12*30 =360 pv = 150000 fv =0 type =0 | ($760.03) | |

present value of 20 year loan on a payment of 760.3 | Using present value function in MS excel | pv(rate,nper,pmt,fv,type) rate = .364% nper = 240 pmt = -760.3 fv =0 type =0 | PV(0.364%,240,-760.03,0,0) | $121,498.59 |

down payment | 150000-121498.59 | 28501.41 |

A house is for sale for $250,000. You have a choice of two 20
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of $25,000, you can obtain a loan at 6% interest, or 2) if you make
a down payment of $50,000 you can obtain a loan at 5% interest.
What is the effective annual rate of interest on the additional
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Mortgages, loans taken to purchase a property, involve regular
payments at fixed intervals and are treated as reverse annuities.
Mortgages are the reverse of annuities, because you get a lump-sum
amount as a loan in the beginning, and then you make monthly
payments to the lender.
You’ve decided to buy a house that is valued at $1 million. You
have $350,000 to use as a down payment on the house, and want to
take out a mortgage for the remainder...

15. Mortgage payments
Mortgages, loans taken to purchase a property, involve regular
payments at fixed intervals and are treated as reverse annuities.
Mortgages are the reverse of annuities, because you get a lump-sum
amount as a loan in the beginning, and then you make monthly
payments to the lender.
You’ve decided to buy a house that is valued at $1 million. You
have $250,000 to use as a down payment on the house, and want to
take out a mortgage...

13. Mortgage payments
Mortgages, loans taken to purchase a property, involve regular
payments at fixed intervals and are treated as reverse annuities.
Mortgages are the reverse of annuities, because you get a lump-sum
amount as a loan in the beginning, and then you make monthly
payments to the lender.
You’ve decided to buy a house that is valued at $1 million. You
have $300,000 to use as a down payment on the house, and want to
take out a mortgage...

13. Mortgage payments
Mortgages, loans taken to purchase a property, involve regular
payments at fixed intervals and are treated as reverse annuities.
Mortgages are the reverse of annuities, because you get a lump-sum
amount as a loan in the beginning, and then you make monthly
payments to the lender.
You’ve decided to buy a house that is valued at $1 million. You
have $200,000 to use as a down payment on the house, and want to
take out a mortgage...

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(ii) the total amount of interest paid: $
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Find (i) The monthly payment: $
ii) the total amount of interest paid: $

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