Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by . Find and interpret your answer. Round your answer to two decimal places.
A) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51.
B) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02.
C) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78.
D) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72.
E) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78.

Question

Suppose that if $100,000 is borrowed to purchase a home, then the monthly payment R is a function of the interest rate i (expressed as a percent) and the number of years n before the mortgage is paid, and is given by  . Find  and interpret your answer. Round your answer to two decimal places. ​
A) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $141.51. 
B) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $4,265.02. 
C) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $277.78. 
D) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $3,801.72. 
E) The monthly payment for $100,000 borrowed for 50 years at 2.25% interest is $278.78.

Quizplus · Accepted Answer

Plugging in the given values into the formula, we get 
$R= \frac{100000 \cdot 0.0225}{1-\left(1+\frac{0.0225}{12}\right)^{-12\cdot 50}}= \frac{2250}{7821.13}= 0.28763...$
$R=\frac{0.0225}{12} \cdot 100000 \cdot \frac{1+\frac{0.0225}{12}}{\left(1+\frac{0.0225}{12}\right)^{12\cdot 50}-1}=\boxed{278.78}$
Therefore, the correct answer is (C) with a monthly payment of $278.78.

Suppose That If $100,000 Is Borrowed to Purchase a Home