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Chapter 8: Problem 24

Make Sense? In Exercises 23-26, determine whether each statement makes sense or does not make sense, and explain your reasoning. There must be an error in the loan amortization schedule for my mortgage because the annual interest rate is only \(3.5 \%\), yet the schedule shows that I'm paying more on interest than on the principal for many of my payments.

Short Answer

Expert verified
The statement makes sense. It is due to the way in which a loan amortization schedule works: initially, more of your payment goes towards interest because the loan balance is higher. As you continue to make payments and the balance decreases, more of your payment is allocated towards paying down the principal.

Step by step solution

01

Understanding Loan Amortization Schedule

In any loan amortization schedule, early payments go primarily towards interest rather than the principal. The interest is calculated on the remaining balance which is high at the beginning. As such, although the interest rate is a relatively low \(3.5\% \), the total amount of interest paid can be high due to the substantial principal balance.
02

Clarification on the distribution of payments

As the loan term progresses, the principal portion of each payment increases as the balance goes down, while the interest portion decreases. It doesn't mean there's an error in the schedule, it is rather the standard method of spreading out the loan repayment over the agreed timeline.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Interest vs Principal
Understanding the flow of your monthly payments towards the interest and the principal is essential when it comes to loan amortization. Initially, a larger portion of your payment is allocated towards paying off the interest rather than reducing the principal balance. This is because the interest charged on a loan is calculated based on the current outstanding principal.

Given a fixed interest rate, like the textbook example of a 3.5% annual rate, the actual dollar amount of interest is higher at the start of the loan because the principal is at its largest. As you continue making payments, the principal slowly decreases, leading to a smaller interest charge, and therefore, more of your payment goes towards reducing the principal. This shift is normal in the life of an amortized loan 鈥� no error in the amortization schedule is implied just because interest payments initially outweigh principal repayments.
Early Payment Interest
When you make early payments on your loan, the savings can be substantial in terms of the interest you avoid paying. The 'interest' portion of your payment schedule is based on the principle that early on, the principal is larger, so more of your payment covers the interest rather than the principal. When you pay extra towards your loan, this extra payment slashes the principal directly.

This reduction in principal means that for all future payments, the interest is computed on a smaller balance, thereby reducing the amount of interest that accrues over the life of the loan. It's a move that can save you money in the long run, particularly for long-term loans like mortgages, where interest can compound extensively over a period of many years.
Mortgage Calculations
Calculating the specifics of a mortgage can seem daunting, but understanding the basic components can clarify the process. The primary factors in mortgage calculations include the loan amount (principal), the interest rate, and the loan term. The monthly payment is derived from an amortization formula that distributes these payments over the course of the loan period, ensuring that by the end of the term, the entire loan is paid off including interest.

Most mortgages are 'fixed-rate' which means that the interest rate does not change over the life of the loan. Others are 'adjustable-rate,' with interest fluctuating with market rates. In either case, an amortization schedule can help you see how each payment breaks down into interest and principal, how much you owe at any point during the loan, and how additional payments will affect your schedule. Overall, mortgage calculations allow you to plan and budget for your long-term financial commitment.

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Most popular questions from this chapter

Exercises 1-2 involve credit cards that calculate interest using the average daily balance method. The monthly interest rate is \(1.5 \%\) of the average daily balance. Each exercise shows transactions that occurred during the March \(1-\) March 31 billing period. In each exercise, a. Find the average daily balance for the billing period. Round to the nearest cent. b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent. c. Find the balance due on April 1 . d. This credit card requires a \(\$ 10\) minimum monthly payment if the balance due at the end of the billing period is less than \(\$ 360\). Otherwise, the minimum monthly payment is \(\frac{1}{30}\) of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by April 9 ? $$ \begin{array}{|l|c|} \hline \text { Transaction Description } & \text { Transaction Amount } \\ \hline \text { Previous balance, } \$ 6240.00 & \\ \hline \text { March 1 } \quad \text { Billing date } & \\ \hline \text { March 5 } \quad \text { Payment } & \$ 300 \text { credit } \\ \hline \text { March 7 } \quad \text { Charge: Restaurant } & \$ 40 \\ \hline \text { March 12 } \quad \text { Charge: Groceries } & \$ 90 \\ \hline \text { March 21 } \quad \text { Charge: Car Repairs } & \$ 230 \\ \hline \text { March 31 } \quad \text { End of billing period } & \\ \hline \text { Payment Due Date: April 9 } & \\ \hline \end{array} $$

In order to pay for baseball uniforms, a school takes out a simple interest loan for \(\$ 20,000\) for seven months at a rate of \(12 \%\) a. How much interest must the school pay? b. Find the future value of the loan.

In Exercises 11-18, a. Determine the periodic deposit. Round up to the nearest dollar. b. How much of the financial goal comes from deposits and how much comes from interest? $$ \begin{array}{|l|l|l|l|} \hline \text { Periodic Deposit } & \text { Rate } & \text { Time } & \text { Financial Goal } \\ \hline \$ ? \text { at the end of each year } & 6 \% \text { compounded annually } & 18 \text { years } & \$ 140,000 \\ \hline \end{array} $$

Exercises 19 and 20 refer to the stock tables for Goodyear (the tire d. How many shares of this company's stock were traded company) and Dow Chemical given below. In each exercise, use yesterday? the stock table to answer the following questions. Where necessary, e. What were the high and low prices for a share yesterday? round dollar amounts to the nearest cent. f. What was the price at which a share last traded when the stock a. What were the high and low prices for a share for the past exchange closed yesterday? b. If you owned 700 shares of this stock last year, what dividend g. What was the change in price for a share of stock from the did you receive? h. Compute the company's annual earnings per share using c. What is the annual return for the dividends alone? How does Annual earnings per share this compare to a bank offering a \(3 \%\) interest rate? $$ =\frac{\text { Yesterday's closing price per share }}{P E \text { ratio }} . $$ $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { 52-Week High } & \text { 52-Week Low } & \text { Stock } & \text { SYM } & \text { Div } & \text { Yld \% } & \text { PE } & \text { Vol 100s } & \text { Hi } & \text { Lo } & \text { Close } & \text { Net Chg } \\ \hline 73.25 & 45.44 & \text { Goodyear } & \text { GT } & 1.20 & 2.2 & 17 & 5915 & 56.38 & 54.38 & 55.50 & +1.25 \\ \hline \end{array} $$

In Exercises 3-4, find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the greater of a standard deduction or an itemized deduction. Suppose your neighbor earned wages of \(\$ 319,150\), received \(\$ 1790\) in interest from a savings account, and contributed \(\$ 4100\) to a tax-deferred retirement plan. He is entitled to a personal exemption of \(\$ 3800\) and the same exemption for each of his two children. He is also entitled to a standard deduction of \(\$ 5950\). The interest on his home mortgage was \(\$ 51,235\), he contributed \(\$ 74,000\) to charity, and he paid \(\$ 12,760\) in state taxes.
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