You plan to take out a 30-year fixed rate mortgage for $225.000. Let P(r) be you
ID: 2744838 • Letter: Y
Question
You plan to take out a 30-year fixed rate mortgage for $225.000. Let P(r) be your monthly payment if the interest rate is r% per year, compounded monthly. Interpret the equations (a) P(4) 1074.18 and (b) P(4) 129.72.
(a) Interpret P(4) 1074.18. Select the correct answer below.
A. If the interest rate on the mortgage is 4%, the monthly payment will be $129.72.
B. If the interest rate on the mortgage is 4%, the monthly payment will be $1074.18.
C. If the interest rate on the mortgage is 5%, the monthly payment will be $1074.18.
D. If the interest rate on the mortgage is 5%, the monthly payment will be $129.72.
(b) Interpret P(4) 129.72. Select the correct answer below.
A. If the interest rate increases from 4% to 5%, the monthly payment will increase by approximately $129.72.
B. If the interest rate decreases from 5% to 4%, the monthly payment will be approximately $1074.18.
C. If the interest rate decreases from 5% to 4%, the monthly payment will increase by approximately $1074.18.
D. If the interest rate increases from 4% to 5%, the monthly payment will decrease by approximately $129.72.
Explanation / Answer
The formula to calculate Monthly Payment = P * r * ( 1 + r )n / [ ( 1 + r )n - 1 ]
Where, P = Principal amount, 225,000
r = monthly rate of interest, for example, 4% = 4 /100 * 12 = 0.0033
n = Number of months = 30 years = 30 * 12 = 360
After inserting the above values in the formula, we get,
Monthly Payment = P * r * ( 1 + r )n / [ ( 1 + r )n - 1 ]
= 225000 * 0.00334 * ( 1 + 0.00334 )360 / [ ( 1 + 0.00334 )360 - 1 ]
= 225000 * 0.00334 * ( 1 .00334 )360 / [ ( 1 .00334 )360 - 1 ]
= 225000 * 0.00334 * 3.3214 / [ 3.3214 - 1 ]
= 225000 * 0.00334 * 3.3214 / 2.3214
= 2496.0321 / 2.3214
= 1,075.22 and nearest answer 1,074.18
Therefore, Answer = " B " that is If the interest rate on the mortgage is 4%, the monthly payment will be $1074.18
Calculation of (b):
Let us try with Interest rate 5% then,
Monthly Payment = P * r * ( 1 + r )n / [ ( 1 + r )n - 1 ]
= 225000 * 0.004166 * ( 1 + 0.004166 )360 / [ ( 1 + 0.004166 )360 - 1 ]
= 225000 * 0.004166 * ( 1 .004166 )360 / [ ( 1 .004166 )360 - 1 ]
= 225000 * 0.004166 * 4.46667 / [ 4.46667 - 1 ]
= 225000 * 0.004166 * 4.46667 / 3.46667
= 4186.8331 / 3.46667
= 1,207.73
The Monthly Payment if the rate of Interest is 5% = 1,207.73
The Monthly Payment if the rate of Interest is 4% = 1,075.22
The Difference = 1,207.73 - 1,075.22 = 132.51 and nearest value 129.72
That is If the Interest Rate inreases from 4% to 5% then, monthly payment increases by $ 129.72
The Answer is " A " If the interest rate increases from 4% to 5%, the monthly payment will increase by approximately $129.72.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.