The monthly payment for a home loan is given by a function f(P,r, N) where P is the principal (the initial size of the loan), r the interest rate, and N the length of the loan in months.Interest rates are expressed as a decimal: A % interest rate is denoted by r = 0.085. If P = 500000, r = 0.085, and N = 276(a 23-year loan), then the monthly payment isf(500000, 0.085, 276) = 788. Furthermore, with these values we haveafӘРEstimate:(a) The change in monthly payment per 2000 increase in loan principal:Afadollars= 0.0077,ofƏr= 8006,(b) The change in monthly payment if the interest rate changes from r = 0.085 to r = 0.075:Afadollars(c) The change in monthly payment if the length of the loan changes from 23 to 25 years:dollarsAfafƏN: -1.6048

Here we have to use total derivative Change if function f(x,y,z) when changes in x is ∆x , changes…

Answered: The monthly payment for a home loan is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Similar questions

Sherri has $1000 to invest for the next 5 years. She can invest it at 4.65% per annum, compounded semi-annually, or at 5.15% per annum, compounded annually, or at 4.25% per annum, compounded quarterly. Calculate Sherri’s earnings for each plan and help her decide which plan is best.
Imagine that you currently have $10,000 in credit card debt. Suppose that your credit card charges 15% APR charged monthly. This means that your monthly interest rate r is given by the formula r=APR/12 If you make payments of $300 per month, how long would it take to pay off your credit card debt?
Many lending agencies compound interest more often than yearly, and as we noted in Example P.2, they are required to report the annual percentage rate, or APR, in a prominent place on the loan agreement. Furthermore, they are required to calculate the APR in a specific way. If r is the monthly interest rate, then the APR is calculated using APR = 12 ✕ r. (a) Suppose a credit card company charges a monthly interest rate of 1.8%. What APR must the company report? (Round your answer to the nearest tenth of a percent.) %(b) The phrase annual percentage rate leads some to believe that if you borrow $5000 from a credit card company which quotes an APR of 21.6%, and if no payments are made, then at the end of 1 year interest would be calculated at 21.6% simple interest on $5000. How much would you owe at the end of a year if interest is calculated in this way? (Round your answer to the nearest cent.)$ (c) If interest is compounded monthly (which is common), then the actual amount you would…
Sally purchases a perpetuity immediate with annual payments that pays $1000 today and Payments increase by 2% per year. She will pay for it with a single payment exactly 3 years from today. Assume a constant force of interest of 10%. Calculate the size of the payment at time 3.
Toni takes out a 30-year mortgage loan for $146,000. Her fixed annual interest rate is 4.3% compounded monthly. Which equation correctly calculates Toni's monthly mortgage payment? 146,000-0.043 М 12|1-(1+) -12-30 0.043 146,000-0.043 M 12/1-(1+ )"] 0.043 146,000-0.043 M = 12{1-()"] 0.043 146,000-0.043 M -12-30 0.043 12 1-
There is a relationship between mortgage amount, number of payments, amount of each payment, how often each payment is made, and the interest rate. The following formula illustrates the relationship: PV= R[1-(1+i)"] i • PV = present value ⚫ i = interest rate per compounding period, as a decimal R = payment amount • n = number of payments Suppose a bank offers you a 3.4% interest rate, compounded semi-annually, on a mortgage amount of $173 112. You pay $1000/mo, or $6000 semi-annually. How long, in years, would it take to pay off the mortgage? a. 80 years b. 60 years c. 20 years od. 40 years e. 10 years A X
Find the Interest rate equivalent to the following: d = 12 1/4% t = 2 years and 3 months t = 450 days
A loan of 500,000 is repaid with 12n equal end of month payments of X. The total amount of principal paid in the nth year is 51308. 042 53. The nominal rate of interest is 3.96% convertible monthly. Find the total interest paid during the life of the loan.
Q.2 The sum of $1000 is deposited every year at 8% simple interest. Calculate the interest at the end of cach year. Do these interest amounts form an A.P?. If so,find the total interest at the end of 30 years. Q.3 A ladder leans against a brick wallI. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree, the angle the ladder makes with the wall.

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