Homework Answers
Add Answer to:
4. Show that in general, the loan balance after the nth payment is Bn= 1.005”Bo –...
4. Show that in general, the loan balance after the nth payment is Bn = 1.005"Bo...
4. Show that in general, the loan balance after the nth payment is Bn = 1.005"Bo – 500(1 + 1.005 + 1.0052 + +1.005n-1), where n = 0, 1, 2, .... 5. We now have an explicit formula for the loan balance after any number of months. Evaluate the geometric sum in Step 4 and show that 1 + 1.005 + 1.0052 + ... + 1.005n-1 = 200(1.005" – 1). Substituting this expression for the geometric sum and letting Bo...
3. At this point we have found a recurrence relation for the sequence of loan balances....
3. At this point we have found a recurrence relation for the sequence of loan balances. We now find an explicit formula for B». Beginning with the first month, we know B1 = 1.005 Bo – 500. After the second payment, the loan balance is B2 = 1.005-B0 - 500(1 + 1.005). Show that after the third payment, the loan balance is B3 = 1.0053B0-500(1 + 1.005 + 1.0052).
i need help answering 1-4! thanks The mathematics of loans 99 Guided Project 45: The mathematics...
i need help answering 1-4! thanks
The mathematics of loans 99 Guided Project 45: The mathematics of loans Topics and skills: Sequences and sums Between houses, cars, or education, most people will take out a loan at some time in their lives. In a typical loan situation, a person borrows an amount $B at a fixed interest rate with a fixed payback period. The borrower makes monthly payments until the loan balance (the amount that remains to be paid) is...
1. Let's take a specific example. Assume you borrow Bo = $15,000 with a fixed annual...
1. Let's take a specific example. Assume you borrow Bo = $15,000 with a fixed annual interest rate of 6%, or 0.5% per month. As a first problem, assume that your monthly payment is $500. The goal is to compute the number of months required to pay off the loan. Every month, two things happen: Interest, which is 0.5% of the current balance, is added to the current balance and the loan balance is decreased by the monthly payment of...
Let ao 2 bo > 0, and consider the sequences an and bn defined by an...
Let ao 2 bo > 0, and consider the sequences an and bn defined by an + bn n20 (1) Compute an+l-bn+1 1n terms of Van-v/bn. (2) Prove that the sequence an is nonincreasing, that the sequence bn Is nonde- creasing, and that an 2 bn for all n 20 (3) Prove that VanVbn S Cr for all n20, where C> 0 and y>1 (give values of C and γ for which this inequality holds). Conclude that an-bn C,γ-n, where...
5) A loan is being repaid by 2n level payments (with the first payment 1 period after the start of the loan) at an...
5) A loan is being repaid by 2n level payments (with the first payment 1 period after the start of the loan) at an effective interest rate of j per period. Just after the nth payment, the outstanding balance on the loan is 3/4 of the initial outstanding balance on the loan. a) Find vj". b) What is the ratio of interest to principal reduction in the n+1st payment? (i.e In+1/PR.n+1)
Let e-Σ (Application of Cauchy product) for x e R. Exercise 21: n-0 a) Show that bk for all b) Let (bn)neNo be the recursion defined by bo - 1 and bn- k-0 n E N. Show that bn-- Hint: Use a) with e*e*...
Let e-Σ (Application of Cauchy product) for x e R. Exercise 21: n-0 a) Show that bk for all b) Let (bn)neNo be the recursion defined by bo - 1 and bn- k-0 n E N. Show that bn-- Hint: Use a) with e*e*1 and the inverse of a power series found in the lecture.
Let e-Σ (Application of Cauchy product) for x e R. Exercise 21: n-0 a) Show that bk for all b) Let (bn)neNo be the recursion...
Suppose that a loan of amount L is being repaid by n installments of R at...
Suppose that a loan of amount L is being repaid by n installments of R at the end of each period. Denote by B. the outstanding loan balance immediately after the tth payment has been made, t=0,1,2,...,n. Then Bo = L, Bn=0, and for t=1,2,...,n, Bi's satisfy the following recurrence relation: B+1= B.(1+i) - R, where i is the interest rate per period. (a) By using (*) to form the sum SBS 1+i)'-s, t=1,2,...,n, (**) show that B = L(1...
PROVE BY INDUCTION Prove the following statements: (a) If bn is recursively defined by bn =...
PROVE BY INDUCTION
Prove the following statements: (a) If bn is recursively defined by bn = bn-1 + 3 for all integers n > 1 and bo = 2, then bn = 3n + 2 for all n > 0. (b) If an is recursively defined by cn = 3Cn-1 + 1 for all integers n > 1 and Co = 0, then cn = (3” – 1)/2 for all n > 0. (c) If dn is recursively defined by...
Compute the new balance of a loan after one monthly payment. Assume that the balance at...
Compute the new balance of a loan after one monthly payment. Assume that the balance at the beginning of the period was $69,535. The monthly payment is $1000. The annual interest rate is 4%.
4. Show that in general, the loan balance after the nth payment is Bn = 1.005"Bo – 500(1 + 1.005 + 1.0052 + +1.005n-1), where n = 0, 1, 2, .... 5. We now have an explicit formula for the loan balance after any number of months. Evaluate the geometric sum in Step 4 and show that 1 + 1.005 + 1.0052 + ... + 1.005n-1 = 200(1.005" – 1). Substituting this expression for the geometric sum and letting Bo...
3. At this point we have found a recurrence relation for the sequence of loan balances. We now find an explicit formula for B». Beginning with the first month, we know B1 = 1.005 Bo – 500. After the second payment, the loan balance is B2 = 1.005-B0 - 500(1 + 1.005). Show that after the third payment, the loan balance is B3 = 1.0053B0-500(1 + 1.005 + 1.0052).
i need help answering 1-4! thanks
The mathematics of loans 99 Guided Project 45: The mathematics of loans Topics and skills: Sequences and sums Between houses, cars, or education, most people will take out a loan at some time in their lives. In a typical loan situation, a person borrows an amount $B at a fixed interest rate with a fixed payback period. The borrower makes monthly payments until the loan balance (the amount that remains to be paid) is...
1. Let's take a specific example. Assume you borrow Bo = $15,000 with a fixed annual interest rate of 6%, or 0.5% per month. As a first problem, assume that your monthly payment is $500. The goal is to compute the number of months required to pay off the loan. Every month, two things happen: Interest, which is 0.5% of the current balance, is added to the current balance and the loan balance is decreased by the monthly payment of...
Let ao 2 bo > 0, and consider the sequences an and bn defined by an + bn n20 (1) Compute an+l-bn+1 1n terms of Van-v/bn. (2) Prove that the sequence an is nonincreasing, that the sequence bn Is nonde- creasing, and that an 2 bn for all n 20 (3) Prove that VanVbn S Cr for all n20, where C> 0 and y>1 (give values of C and γ for which this inequality holds). Conclude that an-bn C,γ-n, where...
5) A loan is being repaid by 2n level payments (with the first payment 1 period after the start of the loan) at an effective interest rate of j per period. Just after the nth payment, the outstanding balance on the loan is 3/4 of the initial outstanding balance on the loan. a) Find vj". b) What is the ratio of interest to principal reduction in the n+1st payment? (i.e In+1/PR.n+1)
Let e-Σ (Application of Cauchy product) for x e R. Exercise 21: n-0 a) Show that bk for all b) Let (bn)neNo be the recursion defined by bo - 1 and bn- k-0 n E N. Show that bn-- Hint: Use a) with e*e*1 and the inverse of a power series found in the lecture.
Let e-Σ (Application of Cauchy product) for x e R. Exercise 21: n-0 a) Show that bk for all b) Let (bn)neNo be the recursion...
Suppose that a loan of amount L is being repaid by n installments of R at the end of each period. Denote by B. the outstanding loan balance immediately after the tth payment has been made, t=0,1,2,...,n. Then Bo = L, Bn=0, and for t=1,2,...,n, Bi's satisfy the following recurrence relation: B+1= B.(1+i) - R, where i is the interest rate per period. (a) By using (*) to form the sum SBS 1+i)'-s, t=1,2,...,n, (**) show that B = L(1...
PROVE BY INDUCTION
Prove the following statements: (a) If bn is recursively defined by bn = bn-1 + 3 for all integers n > 1 and bo = 2, then bn = 3n + 2 for all n > 0. (b) If an is recursively defined by cn = 3Cn-1 + 1 for all integers n > 1 and Co = 0, then cn = (3” – 1)/2 for all n > 0. (c) If dn is recursively defined by...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago