Question

Prof. Chaos finds a new house he wants to buy for $260,000. After selling his current house he expects to have $80,000 as a down payment for his new house. What would Prof. Chaos monthly payment be on the $180,000 mortgage he would need if he takes out a 30-year fixed rate mortgage at a 4% nominal annual rate? (round your answer to the nearest cent)

Answer 1

The monthly payment of the prof. Chaos on $1,80,000 would be$259.348.

What is the present value?

The value in the presence of a sum of money, in opposition to some future value it will have when it has been invested at compound interest.

The formula for finding present value is:

$\text{Present Value}=A\times[\dfrac{\rm{(1+i)^n}-1}{i(1+i)^n}]$

Computation of the chaos's monthly payment.

Given that,

Present Value =  $180,000,

time = 30 years,

rate = 4%.

It is given that the payment would be paid monthly, then we have to convert the time and the rate of interest to monthly.

Time =360 (30 years x 12 months per year),

Rate=

$=\dfrac{0.3333333}{100} \\\\\\=0.003333333$

Now, put the values given in the above formula :

$\text{Present Value}=A\times[\dfrac{\rm{(1+)^n}-1}{i(1+i)^n}]\\\\\\\ 1,80,000=A\times[\dfrac{\rm{(1+0.0033)^{360}}-1}{0.0033(1+0.0033)^{360}}]\\\\\\A=\ 259.348.$

Therefore, the total amount of $259.348 is required to pay monthly for the full payment of $1,80,000.

Learn more about present value, refer:

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