ewton's method and the following formula are used to calculate the true interest rate of a loan, where P is the amount of the loan, n is the number of monthly payments, and M is the payment amount. Find i, and 1-(1+i)-nP f(i) = M = 600, M = 54, n= 12, and i, =0.01 Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

ewton's method and the following formula are used to calculate the true interest rate of a loan, where P is the amount of the loan, n is the number of monthly payments, and M is the payment amount. Find i, and 1-(1+i)-nP f(i) = M = 600, M = 54, n= 12, and i, =0.01 Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 31E: Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is...

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Kyoko has 10,000 that she wants to invest. Her bankhas several investment accounts tochoose from, allcompounding daily. Her goal is to have 15,000 bythe time she finishes graduate school in 6 years. Tothe nearest hundredth of a percent, what should herminimum annual interest rate be in order to reach hergoal? (Hint: solve the compound interest formula forthe interest rate.)
Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.
Equity in a Home When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. Technically, the lending agency calculates your equity by subtracting the amount you still owe on your mortgage from the current value of your home, which may be higher or lower than your principal. Assume that your mortgage is for 350, 000 at a monthly rate of 0.007 as a decimal and that the term of the mortgage is 30 years. Then your equity after k monthly payments is 350, 0001.007k-11.007360-1 dollars. Calculate the equity in your home after 10 years.
The Truth in Lending Act 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 APR is calculated using APR=12r. a. Suppose a credit card company charges a monthly interest rate of 1.9%. What APR must the company report? b. The phrase annual percentage rate leads some people to believe that if you barrow 6000 from a credit card company that quotes an APR of 22.8%, and if no payments are made, then at the end of 1 year, the interest would be calculated as 22.8% simple interest on 6000. How much would you owe at the end of a year if interest is calculated in this way? c. If Interest is calculated monthly which is common, then the actual amount you would owe in the situation of part b is given by 60001.01912. What is the actual amount you would owe at the end of a year?
An Amortization Table Suppose you borrow P dollars at a monthly interest rate of r as a decimal and wish to pay off the loan in t months. Then your monthly payment can be calculated using M=Pr(1+r)t(1+r)t1 dollars. Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow 3500 at a 9 APR meaning that you use r = 0.09/12 in the preceding formula and pay it back in 2 years. a. What is your monthly payment? b. Lets look ahead to the time when the loan is paid off. i. What is the total amount you paid to the bank? ii. How much of that was interest? c. The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by B=P((1+r)t(1+r)k(1+r)t1) dollars. i. How much do you still owe the bank after 1 year of payments? ii. An amortization table is a table that shows how much you still owe the bank after each payment. Make an amortization table for this loan.
The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.