Interest Rates

From this web page, you can get a better understanding of interest rates, and as a result, your options. The information goes from simple to complicated so you can find your own level. I urge all readers to at least glance at the whole page. You never know what you may learn.

  • For Beginners
  • For Novices
  • For Experts
  • For Beginners

    For those who find the subject of borrowing confusing, it is really very simple. When you borrow money, it is natural for the lender to want to charge you money for this. The more you borrow, the more it costs the lender. He could have put the money in the bank instead. He must charge you an amount that beats what the bank would give him plus his expenses for doing business. After all, he could have been employed elsewhere. Whatever his reason for charging so much, you do not want him to charge too much. Shop around so that you can find a lender who is not too greedy (or perhaps the least greedy).

    When you apply for a loan, you want to maximize the chance that it will be accepted. To do this, you must convince the lender that you can and want to pay it back. Making a high salary helps, because it means you have plenty of after tax income. Having few expenses helps, too. This convinces him that you CAN pay it back. How do you demonstrate that you WANT TO pay it back? One way is to show a history of paying your debts on time. Even paying apartment rent on time helps. Another way is to put up collateral. If you borrow money to buy a durable good (for example, furniture), making that good the collateral means that if you do not pay the money back as agreed, the lender can take it. The lender does not want it, but he knows that you want it. This is your incentive to pay the money on time.

    The loan is more affordable if the interest is tax deductible. The only way to do this is to make your home the collateral. Then you fill out your income tax return and list the interest part of your payments on Schedule A. It gets subtracted from your income before your tax is computed. For every $1000 of interest, you will get back at least $150 as long as you have taxes to pay.

    The math for interest rate calculations is very easy as long as you do not bite off more than you can chew. Let's do a simple example. You borrow $5000 to buy a car. You will pay it back over 2 years. The interest rate is 10%. If only the interest rate were 0%. Then you can pay just $5000 over 2 years. $5000/24 months=$208 per month. Common sense tells you that this is lower than you will pay. The interest expense is 10% times $5000=$500 per year. This is $42 per month. $42 for the interest plus $208 for the principal (amount borrowed) is $250. This is higher than you will pay, because the interest expense goes down as you pay off the loan. Now you know that your payment will be between $208 and $250. The right answer is $231, so this is a good approximate method.

    Another good approximation comes in handy when you buy a house. Suppose you borrow $100,000 at 8% interest. You will pay this off in 30 years. Your interest expense is 8% times $100,000=$8000 per year or $667 per month. The right answer is $734 per month. For 30 year loans, do not bother to include the principal. If you do, you will add $100,000/360 months=$278 per month. The total is $945. This is way above $734, so this is inaccurate. Just remember that you will pay $667 plus a little more. Actually, you should include tax deductibility here. If you are in the 15% tax bracket, then you will get back 15% times $667=$100. $667 - $100=$567. Your net monthly payment is $567 plus a little more. (The exact answer is $634.)

    For Novices

    You already know that you should try to get the best after tax interest rate. Despite this, you find yourself mired in credit card debt. How do you manage a decent rate? As discussed in Managing Debt, you could look for another credit card with a lower interest rate. After doing this, there is a way to reduce the interest rate to 0%. It is called PAY YOUR BILLS ON TIME. I know this is tough, but you should work toward this goal. Once you get there, you can buy something, wait about a month, then pay for it. As long as you pay on time, you get one month of interest free money on everything you buy. After this, you can look for a credit card with no fee and one that gives you a rebate. Credit card companies are very generous to responsible people, because there are so few of them.

    If you are having trouble getting a credit card with a low interest rate, you may want to improve the rate with a personal, or signature, loan. With these loans, you will be required to pay the money back in an agreed upon time. The shorter the time, the lower the interest rate. For example, if you agree to pay the money back in five years, the interest rate may be 12%. If you agree to three years, it would become 11%. Forget the actual rate. That varies all the time. Remember that you can make it drop by 1% by paying it back faster.

    If you want a better rate, you can get a car loan. Using the car as collateral saves you money. As with the personal loan, the rate depends on the term. Now the rate also depends on the down payment. The interest rate varies approximately as in Table 1 below.

     Loan          Percent of Car Price Borrowed
     Term            80%       90%       100%
    2 years          7.5%      7.7%      7.9%
    3 years          7.9%      8.1%      8.3%
    4 years          8.3%      8.5%      8.7%
    5 years          8.7%      8.9%      9.1%
    Table 1.  Interest Rate versus Loan Term and Amount Financed

    As you can see, if you borrow 80% of the price of the car for two years, you will pay 7.5% interest. If you borrow 100% for five years, you will pay 9.1%. 1.2% of the difference is from the lengthened term and 0.4% is from the lack of down payment. To try and make this difference more vivid, suppose you buy a car for $10,000. You consider putting $2000 down and borrowing the rest for two years. You learn that your monthly payments will be $360, so you change your mind. You will put down nothing and pay over a five year period. Now, your monthly payments will be $208. You accept this, but you really should not. You will end up paying $12,480. In the first deal, you pay only $10,640. You lose $1840. How can you save this money? Suppose you can afford the $360 monthly payment. Delay the purchase and pay yourself the $360. In 5.5 months, you will have saved the $2000 down payment.

    The concepts discussed above are also true for mortgages. To get the best interest rate, you want the shortest possible term and the largest possible down payment. To give you some idea of how important this is, Table 2 shows approximate interest rate variations for these parameters.

     Loan                        Percent of House Price Borrowed
     Term                        less than 80%     more than 80%
    1 year ARM                  5.5% + 3 points   6.0% + 3 points
    5 years fixed, then ARM     7.5% + 3 points   8.0% + 3 points
    15 years                    7.5% + 3 points   8.0% + 3 points
    30 years                    8.0% + 3 points   8.5% + 3 points
    Table 2.  Mortgage Interest Rate versus Loan Term and Amount

    In the above table, the term ARM stands for adjustable rate mortgage. Every year, it adjusts to adhere to new interest rates. This is not for people who are squeamish about the economy. To placate such people, some mortgages fix the rate for five years, then vary it. This way the borrower has five years of pay raises to prepare for the shock. Unfortunately, it requires about a 2% higher interest rate. The 30 year mortgage requires 0.5% more than that. To get a break, one can opt for a 15 year mortgage, but the monthly payments are somewhat higher.

    If one borrows more than 80% of the house value, the lender often insists on mortgage insurance. The lender knows that his investment is protected if the borrower has at least 20% of equity in the house. If the lender needs to foreclose, he is certain to find a buyer who will pay at least 80% of the house value. Without this equity, the lender needs mortgage insurance for protection. It costs about 0.5% of the house price.

    The term "points" in Table 2 refers to a charge in addition to the interest rate. In the example of Table 2, the borrower must pay 3% of the loan amount in the beginning of the loan. It is possible to get a higher rate with no points or a lower rate with more points. Which should you do when? If you are refinancing a house that you already own, your points are deductible from your taxes gradually over the life of the loan. This is unfair and costly, so get a loan with no points. If you are having trouble making the down payment, get a loan with no points. Otherwise, get a loan with points.

    Another addition to the interest rate occurs if the amount borrowed is above about $200,000. For such a loan, called a jumbo loan, the rate goes up by about 0.5%. It also rises by the same amount if you want a low documentation loan. Here, you can ask that the lender verify just your income or just your wealth. The lender must be compensated for the extra risk.

    How does the lender decide how much money you can borrow? Primarily, he looks at your income. Suppose you earn $50,000 per year. He computes 28% of $50,000=$14,000 per year=$1167 per month. This is the principal and interest that you can afford. If you get an 8%, 30 year mortgage, then you can borrow $159,000. Suppose you know that your real estate taxes and homeowner's insurance will be only $150 per month. The payment including this can be as high as 33%. 33% of $50,000=$17,500 per year=$1458 per month. This leaves $1308 for principal and interest. Now you can borrow $178,000. Suppose you have no other debts. Now your payment can be as high as 38% of $50,000, which is $19,000 per year or $1583 per month. You can borrow $195,000. The percentages vary, but for this example:

     your principal and interest must be below 28% of your income
     your mortgage payment must be below 33% of your income
     all of your payments to anyone must be below 38% of your income.

    For Experts

    As experts, you are ready to see the formula to compute the monthly payment corresponding to a loan. You need no longer depend on look up tables to find out how much you will pay. In fact, you can now make up your own look up tables.

         The monthly payment formula is
         M = P*i*(1+i)**n/[(1+i)**n - 1]
    where M is the monthly payment to repay the loan,
          P is the amount borrowed,
          i is the interest rate per MONTH,
          n is the number of monthly payments,
          * means multiply, and
          ** means to the power of.

    For example, if $1000 is borrowed at 6% annual interest and it is to be paid back over 2 years, then P=$1000, i=6%/12=0.5%, and n=24 months.

         M= ----------------------- = $44.32

    Now you can figure out your monthly payment from any loan you might be considering. Alternately, you can figure out from the monthly payment you can afford, how much money you can borrow. If carrying this formula around is inconvenient, you may want to make a table like the one below.

                 A N N U A L   I N T E R E S T   R A T E
    Years      5%        6%        7%        8%        9%        10%
       2     43.87     44.32     44.77     45.23     45.68     46.14
       3     29.97     30.42     30.88     31.34     31.80     32.27
       4     23.03     23.49     23.95     24.41     24.89     25.36
       5     18.87     19.33     19.80     20.28     20.76     21.25
      10     10.61     11.10     11.61     12.13     12.67     13.22
      15      7.91      8.44      8.99      9.56     10.14     10.75
      30      5.37      6.00      6.65      7.34      8.05      8.78
    Table 3.  Monthly Payment per $1000 Borrowed

    To give you an idea how this table can come in handy, suppose you go to the car dealer and agree to buy a car with a $10,000 loan at 9% for 3 years. Your table says that the monthly payment should be $31.80 for $1000, so it would be $318.00 for your loan. The dealer uses his table and accidentally (yeah, right) uses the 10% column. He announces the payment will be $322.70. Without your table, you would never know you were paying too much.


    Copyright 1996 Alacrity Research