Answer:
Monthly payment would be $ 405.35
Explanation:
Given,
The price of the house = $ 100,000,
Down payment percentage = 20%,
So, the amount of down payment = 20% of price of the house
= 20% of $ 100,000
[tex]=\frac{20\times 100000}{100}[/tex]
= $ 20000,
Thus, the present value of the loan, PV = price of the house - down payment
= $ 100,000 - $ 20000
= $ 80,000
Number of years = 30,
∴ Number of months, n = 30 × 12 = 360,
Annual rate = [tex]4\frac{1}{2}\%[/tex] = 4.5% = 0.045,
∴ monthly rate, r = [tex]\frac{0.045}{12}[/tex]
Therefore, the monthly payment of the loan,
[tex]P = \frac{PV(r)}{1-(1+r)^{-n}}[/tex]
[tex]=\frac{80000(\frac{0.045}{12})}{1-(1+\frac{0.045}{12})^{-360}}[/tex]
≈ $ 405.35 ( using calculator )
The monthly payment would be $405.35
It refers to how much one should invest today in order to get the expected return in the future. It is based on the time value of the money concept, i.e. the value of $1 is not the same as the value of $1 in the future, which means the purchasing capacity will decrease in the future as compared to today.
Given,
Investment required to purchase the house= $100,000,
Down payment percentage = 20% of the house price
= 20% of $100,000
=$20,000
Thus, the present value of the loan (PV) = Purchase Price of the house - down payment
= $100,000 - $20,000
= $80,000
No. of years = 30,
No. of months (n) = 30 × 12 = 360,
Annual Discounted/ Interest rate = 4 1/2% = 4.5% = 0.045,
monthly Discounted/ Interest rate, (r) = 0.045/12
Therefore, the monthly payment of the loan,
= $405.35 (using calculator)
Learn more about present value of the annuity method here:
https://brainly.com/question/24452710
