1. Managing Money 4

2. Loan Payments, Credit Cards, and Mortgages
Unit 4D
Loan Payments, Credit Cards, and Mortgages

3. Loan Basics
The principal is the amount of money owed at any particular time.
An installment loan (or amortized loan) is a loan that is paid off with equal regular payments.
The loan term is the time you have to pay back the loan in full.

4. Loan Payment Formula (Installment Loans)
PMT = regular payment amount
P = starting loan principal (amount borrowed)
APR = annual percentage rate
n = number of payment periods per year
Y = loan term in years
The derivation of this formula can be done by simply setting the compound interest formula equal to the annuity formula and is fairly approachable for many students. Again, working through realistic scenarios that students can relate to will help them appreciate the importance of this payment formula.

5. Principal and Interest for Installment Loans
The portions of installment loan payments going toward principal and toward interest vary as the loan is paid down.
Early in the loan term, the portion going toward interest is relatively high and the portion going toward principal is relatively low.
As the term proceeds, the portion going toward interest gradually decreases and the portion going toward principal gradually increases.

6. Example
Suppose you have student loans totaling $7500 when you graduate from college. The interest rate is APR – 9%, and the loan term is 10 years. What are your monthly payments? How much will you pay over the lifetime of the loan? What is the total interest you will pay on the loan?

7. Example (cont)
Solution We use the loan payment formula to find the monthly payments:

8. Example (cont)
Your monthly payments are $ Over the 10-year term, your total payments will be

9. Example (cont)
Of the $11,401.20, $7500 pays off the principal. The rest, or $11,401 – $7500 = $3901, represents the interest payments.

10. Table of First Three Months
For the student loan in the previous example, the table shows the amount of the payment that is applied to the principal. It is easier to use software that find principal and interest payments with built-in functions.
Although many financial institutions will provide the individual with an amortization schedule upon initiating the loan, there may be two important reasons that students should be able to follow the simple mathematics of a schedule. 1) Once they gain a little confidence with the flow of the columns, they are in a position to modify their own schedules using Excel or some other software and customizing it to facilitate their personal strategies of making additional payments of principal. 2) It would also be important to periodically check the accuracy of the lending institution’s monthly or annual statements to verify that everything is legitimate and up to date.

11. Credit Cards A minimum monthly payment is required.
Credit cards differ from installment loans in that you are not required to pay off your balance in any set period of time.
A minimum monthly payment is required.
Monthly payment generally covers all the interest but very little principal.
It takes a very long time to pay off a credit card loan if only the minimum payments are made.

12. Example
Suppose you have a credit card balance of $2300 with an annual interest rate of 21%. You decide to pay off your balance over 1 year. How much will you need to pay each month? Assume you will make no further credit card purchases.
Solution
You must pay $ per month to pay off the balance in 1 year.

13. Mortgages
A home mortgage is an installment loan designed specifically to finance a home.
The down payment is the amount of money you must pay up front in order to be given a mortgage or other loan.
Closing costs are fees you must pay in order to be given the loan. These include
direct costs, or fees charged as points, where each point is 1% of the loan amount.

14. Mortgages
A fixed rate mortgage is one in which the interest rate is guaranteed not to change over the life of the loan.
An adjustable rate mortgage is one where the interest rate changes based on the prevailing rates.

15. Example
Great bank offers a $100,000, 30-year, 5% fixed rate loan with closing costs of $500 plus 1 point. Big Bank offers a lower rate of 4.75% on a 30-year loan, but with Great Bank closing costs of $1000 plus 2 points. Evaluate the two options.
Solution
Great Bank

16. Example (cont)
Great bank offers a $100,000, 30-year, 5% fixed rate loan with closing costs of $500 plus 1 point. Big Bank offers a lower rate of 4.75% on a 30-year loan, but with closing costs of $1000 plus 2 points. Evaluate the two options.
Big Bank:

17. Example (cont)
You will save about $15 per month with Big Bank’s lower interest rate. Now we must consider the difference in closing costs. Big bank charges an extra $500 plus an extra 1 point (1%), which is $1000 on this loan. Big Bank cost an extra $1500 up front. We divide this to find the time it will take to recoup this extra $1500.
Unless you are sure you will be staying in the house for much more than 8 years, it is most wise to go with Big Bank.

18. The Relationship Between Principal and Interest for a Payment
Understanding the relationship between interest and principal and especially the general shape of the two curves is vital. The difference between home and car loans can also be pointed out due to the length of the loan process.
Portions of monthly payments going to principal and interest over the life of a 30-year $100,000 loan at 5%

19. Example
You have a choice between a 30-year fixed rate loan at 4% and an ARM with a first-year rate of 3%. Neglecting compounding and changes in principal, estimate your monthly savings with the ARM during the first year on a $100,000 loan. Suppose that the ARM rate rises to 5% by the third year. How will your payments be affected?

20. Example (cont) Solution
Since mortgage payments are mostly interest in the early years of a loan, we can make approximations by assuming that the principal remains unchanged. For the 4% fixed rate loan, the interest on the $100,000 loan for the first year will be approximately 4% × $100,000 = $4000. With the 3% ARM, your first-year interest will be approximately 3% × $100,000 = $3000. The ARM will save you about $1000 in interest during the first year, which means a monthly savings of about $1000 ÷ 12 ≈ $83.

21. Example (cont)
By the third year, when rates reach 5%, the situation is reversed. The rate on the ARM is now 1 percentage point above the rate on the fixed rate loan. Instead of saving $83 per month, you’d be paying $83 per month more on the ARM than on the 4% fixed rate loan. Moreover, if interest rates remain high on the ARM, you will continue to make these high payments for many years to come. Therefore, while ARMs reduce risk for the lender, they add risk for the borrower.