The Smothers are looking at retiring and would like to be debt free when this st

Question

The Smothers are looking at retiring and would like to be debt free when this starts. They presently owe $225,000 on their home mortgage that has a rate of 4.25% APR with monthly compounding. a If they make payments of $3,000 monthly, how many years until they can retire (when the house loan is paid off). b If in the upcoming 5 years, they make $2,000 monthly payments, and then sell their house for $500,000, how much will they have to buy a home in a retirement development? (All taxes and fees should be ignored) The Smothers are looking at retiring and would like to be debt free when this starts. They presently owe $225,000 on their home mortgage that has a rate of 4.25% APR with monthly compounding. a If they make payments of $3,000 monthly, how many years until they can retire (when the house loan is paid off). b If in the upcoming 5 years, they make $2,000 monthly payments, and then sell their house for $500,000, how much will they have to buy a home in a retirement development? (All taxes and fees should be ignored)

Explanation / Answer

Hi,

Please find the answer with excel calculations as follows:

Part A:

PMT = 3000 (indicates monthly payments)

Rate = 4.25%/12 (indicates monthly interest rate)

PV = 225000 (indicates the present value of loan)

FV = 0 (indicates the future value of loan, if any)

Nper = ? (indicates the number of years, to be calculated)

Years Until they Retire = Nper(Rate,PMT,PV,FV)/12 = Nper(4.25%/12,3000,-225000,0)/12 = 7.28 Years

Note: We divide the equation by 12 so that we can get the number of years.

Part B:

In this case, you need to calculate the future value of monthly payments at the end of 5 Years.

PMT = 2000 (indicates monthly payments)

Rate = 4.25%/12 (indicates monthly interest rate)

PV = 225000 (indicates the present value of loan)

Nper = 5*12 = 60 (indicates the period))

FV = ? (indicates the future value of loan)

Years Until they Retire = FV(Rate,Nper,PMT,PV) = FV(4.25%/12,60,2000,225000) = 411609

Since the house is sold for 500000, we can say that the couple will have = 500000 - 411609 = 88391

Thanks.

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