Richard Miyashiro purchased a condominium and obtained a 20-year loan of $196,000 at an annual interest rate of 8.30%. (Round your answers to the nearest cent.)

(a) What is the mortgage payment? $

(b) What is the total of the payments over the life of the loan? $

(c) Find the amount of interest paid on the mortgage loan over the 20 years. $

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slicergiza slicergiza · Answer 1 · 2019-09-12T08:04:23+02:00

Answer:

(a) $ 1,676.21

(b) $ 402,289.22

(c) $ 206,289.22

Step-by-step explanation:

Given,

The present amount of the loan, PV = $ 196,000

Time = 20 years,

So, the number of months, n = 12 × 20 = 240

Also, the annual rate = 8.30 % = 0.083,

So, the monthly rate, r = [tex]\frac{0.083}{12}[/tex]

(a) Hence, the mortgage payment or monthly payment,

[tex]P=\frac{(PV)r}{1-(1+r)^{-n}}[/tex]

[tex]P=\frac{196000(\frac{0.083}{12})}{1-(1+\frac{0.083}{12})^{-240}}[/tex]

[tex]=\$ 1676.20508437[/tex]

[tex]\approx \$ 1676.21[/tex]

(b) The total payment = monthly payment × number of periods

= 402289.220249

≈ $ 402,289.22

(c) Interest paid = total payment - present value of loan

= 402289.22 - 196,000

= $ 206,289.22