Using Loans and Credit to Make Purchases
Chapter 12: Using Loans and Credit to Make Purchases
For instance, if you need $50,000 to cover expenses for 3 months, and you arrange for a discount note charging 10% interest, you don’t get the full $50,000 to work with. Instead, you get $50,000 minus the interest charge. So, instead of borrowing $50,000, you need to increase the amount of the note to an amount that allows you to end up with $50,000 after the interest is subtracted.
To find out how much you need to increase the note by, consider the follow- ing: The $50,000 you want is the difference between the face value of the note and the interest paid. Let frepresent the face value and Ithe amount of inter- est. Three months is one-quarter of a year, or 0.25.
So here’s what the equation would look like:
$50,000 = f– I
= f– (f×0.10 ×0.25)
You replace the amount of interest, I, with the face value times the interest rate of 10% times the quarter year. Now you’re ready to solve for the value of f:
, . .
, .
, .
. ,
. . , .
f f
f f
f f f
50 000 0 10 0 25
50 000 0 025 50 000 0 975
0 975 50 000
0 975 0 975 51 282 05
# #
.
= -
= -
=
=
^ h
As you can see, if you arrange to borrow about $51,282, you’ll have your
$50,000 to work with during those 3 months.
Borrowing with a Conventional Loan
A conventional loanmay come in the form of a mortgage on a building, a car or truck loan, a building equity loan, or a personal loan. Loans are available through banks, credit unions, employers, and many other institutions. Your task is to find the best possible arrangement to fit your needs. If you’re com- fortable doing the legwork and computations yourself, get out paper, pencil, and a calculator and start searching the newspaper and Internet. If you don’t trust yourself quite yet, find an accountant or financial consultant whom you trust and feel comfortable talking to.
You can compute the interest and payments of a loan by using a book of tables and your handy, dandy calculator, or you can even find a loan calcula- tor on the Internet. The variables involved in the computation of loan pay- ments are
Amount of money borrowed Interest rate
Amount of time needed to pay back the loan
Each of these variables (values that change the result) affects the result differently — some more dramatically than others.
Dealing with a bank or financial institution may seem more impersonal than dealing with an acquaintance or small lender, but the trade-off is more flexi- bility in payment schedules, availability of more money, and, usually, better rates and terms of the loan.
Computing the amount of loan payments
You can determine the amount of your loan payments using tables of values or a loan calculator. If you’re more of a control person (like me), you proba- bly want to do the computations yourself — just to be sure that the figures are accurate.
The periodic payment of an amortized loan is determined with this formula:
R i
Pi
1 1 n
= -^ + h-
where Ris the regular payment you’ll be making, Pis the principal or amount borrowed, iis the periodic interest rate (the annual rate divided by the number of times each year you’re making payments), and nis the number of periods or payments.
Try your hand at determining a payment with this example: What’s the monthly payment on a loan of $160,000 for 10 years if the interest rate is 9.75% compounded monthly?
The interest rate per month is 9.75% ÷ 12 = 0.8125%, or 0.008125 per interest period. The number of payments, n, is 10 years ×12 = 120. Using all the values in the formula, you get:
.
, .
.
, , .
R 1 1 0 008125 160 000 0 008125
0 621319 1 300
2 092 32
= 120
- + - = =
^
^ h
h
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Chapter 12: Using Loans and Credit to Make Purchases
So the monthly payments are about $2,100. To find the total payback, simply multiply the monthly payment by the number of payments: $2,092.32 ×120 =
$251,078.40. So more than $91,000 is paid in interest. (The interest is the total payback minus the amount borrowed: $251,078.40 – $160,000 = $91,078.40.)
Considering time and rate
There’s no question that the amount of money borrowed affects the condi- tions of a payback. After all, the more you borrow, the more you’re going to owe. But the rate of interest and amount of time needed to repay the money act a bit differently in the overall payback. I explain both of these in the fol- lowing sections.
Taking your time to repay a loan
Spreading your loan over a longer period of time makes your regular pay- ments smaller. But what does spreading out those payments do to the total amount of the payback? And how does spreading out the payments affect the total amount of interest? Well, it only makes sense that the longer you take to repay a loan, the more you’re going to pay for the privilege of doing so.
Table 12-1 gives you an example of how time affects payback — both in the monthly payments and the total amount repaid. The figures in Table 12-1 are all based on a loan of $40,000 at 9% interest compounded monthly.
Table 12-1 Stats on a Loan for $40,000 at 9% Interest in Monthly Payments
Number of Years Monthly Payments Total Payback Total Interest
10 $506.70 $60,804.37 $20,804.37
15 $405.71 $73,027.19 $33,027.19
20 $359.89 $86,373.69 $46,373.69
25 $335.68 $100,703.60 $60,703.60
30 $321.85 $115,865.70 $75,865.70
35 $313.60 $131,710.82 $91,710.82
40 $308.54 $148,101.40 $108,101.40
As you can see from Table 12-1, the payments are much smaller if you pay back in 40 years rather than in 10 years. But the amount of interest paid is enormously greater when spread over the longer period of time.
Showing an interest in the interest rate
As astounding as increasing the amount of time to repay a loan can be in terms of interest paid, an increase in the interest rate tends to be just as astonishing. For instance, increasing the rate by only 1% makes a significant difference when you’re paying over a multiyear period.
Table 12-2 shows you what happens to a $40,000 loan as the interest rate increases. In the table, you see the total payback and interest paid if the loan is for 10 years and if the loan is for 30 years.
Table 12-2 Stats on a Loan for $40,000 for 10 Years and 30 Years
Interest Rate Total at 10 Years (Interest) Total at 30 Years (Interest) 6% $53,289.84 ($13,289.84) $86,335.28 ($46,335.28) 7% $55,732.07 ($15,732.07) $95,803.56 ($55,803.56) 8% $58,237.25 ($18,237.25) $105,662.10 ($65,662.10) 9% $60,804.37 ($20,804.37) $115,865.70 ($75,865.70) 10% $63,432.35 ($23,432.35) $126,370.30 ($86,370.30) 11% $66,120.01 ($26,120.01) $137,134.60 ($97,134.60) 12% $68,866.06 ($28,866.06) $148,120.20 ($108,120.20)
Table 12-2 confirms it: The higher the interest rate, the more you pay in inter- est. At 6% and 30 years, you pay a little more than twice what you borrowed after adding interest. At 12% and 30 years, you pay over $100,000 more than you borrowed just in interest.
Determining the remaining balance
If you borrow money using a 20- or 30-year loan and then, all of a sudden, you have a windfall and want to clear all your debts, you need to know what’s left to pay on your loan. You may not expect to win the lottery, inherit a fortune, or receive some other type of windfall when you take out a loan, but you really should avoid any contracts that penalize you for making an early payment.
Get rid of that type of clause, if you can. It won’t hurt anything if you do get that windfall, and you’ll save money if you’re able to settle up before the end of the loan term. By paying early, you avoid paying some of the interest.
However, most amortized loans build in high interest payments at the begin- ning of the payback. So you want to get that windfall early in the game.
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Chapter 12: Using Loans and Credit to Make Purchases
You can find the approximate balance remaining on a loan by using this formula:
B R i
i 1 1 (n x)
= R -^ + h- - T
SSS
V X WWW
where Bis the remaining balance on the loan, Ris the regular payment amount, iis the periodic interest rate, nis the number of payments, and xis the number of payments that have already been made.
Say that you’ve been paying off a 20-year loan and are 10 years into the pay- ments. You think you have close to half the loan paid, right? Wrong! Check out the following example to see why you aren’t so close to having your loan paid off.
Ten years ago, you took out a 20-year loan for $60,000 at 7.25%. You make monthly payments of $475. But now you’ve inherited some money and want to pay off the balance of the loan. How close is the balance to being halfway paid off?
To find out, you use the formula to estimate the remaining balance. First figure out the values of all the known variables. The value of iis 7.25% ÷ 12 ≈ 0.604167%, or 0.00604167; n= 20 ×12 = 240; and x= 10 ×12 = 120. Now you’re ready to plug all these numbers into the formula and solve. Your math should look like this:
. .
. .
.
. .
, . B 475
0 00604167 1 1 0 00604167
475 0 00604167 1 1 00604167
475 0 00604167
0 514618 475 85 178105 40 459 60
(240 120)
120
.
= - +
= -
= =
- -
-
^
^
h
h R
T SSS R T SSS
; 6
V X WWW V X WWW
E @
Halfway through the loan period of 20 years, only one-third of this loan has been paid off. Yikes!
Paying more than required each month
Say that you’ve taken out a loan and arranged for monthly payments over a 20-year period. Then you realize that you’re able to pay a little more than the monthly payment. Is it a good idea to do so? Absolutely! Making payments larger than necessary is a splendid idea. You’ll finish paying off the loan much sooner, and you’ll save lots of money in interest.
Making larger-than-necessary payments reduces the amount of the principal still owed, which in turn reduces the interest that needs to be paid. Why?
Because the monthly interest is figured based on the current principal, and the interest is paid first. Anything left goes toward reducing the principal. At the beginning of an amortized loan schedule, most of the payment goes toward interest.
Table 12-3 shows you how much of a payment on a 20-year, $100,000 loan at 6% goes toward interest and how much goes toward the principal. The monthly payments are about $716.44.
Table 12-3 Principal and Interest on a $100,000 Loan
Principal Interest That Month Payment – Interest = Applied to Principal
$100,000 $500 $716.44 – 500 = $216.44
$99,783.56 $498.92 $716.44 – 498.92 = $217.52
$99,566.04 $497.83 $716.44 – 497.83 = $218.61
↓ ↓ ↓
$2,128 $10.64 $716.44 – 10.64 = $705.80
$1,422.20 $7.11 $716.44 – 7.11 = $709.33
$712.87 $3.56 0
You see that most of the payment goes toward interest at the beginning of the 20 years. Toward the end, most of the payment goes toward the principal.
The last payment is only $712.87. By increasing the payment to $800 each month, the additional $83.56 goes toward reducing the principal. This way, the loan is paid off in about 16.5 years instead of 20. And the total amount of interest paid is reduced.
To figure out how much interest is saved, multiply the payment amount by the total number of payments you’ll make in 20 years (20 ×12 = 240 pay- ments): $716.44 ×240 = $171,945.60. The loan is for $100,000, so $71,945.60 is paid in interest. The number of payments in 16.5 years is 16.5 ×12 = 198. By increasing the payments to $800, you end up paying $800 ×198 payments =
$158,400. The interest paid this time is $58,400. The savings is over $13,500.
How did I get the number of payments needed at $800? The easiest way to figure this out is with a spreadsheet and formulas that you type in for the interest and payments. I explain how to set up spreadsheets in Chapter 5.
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Chapter 12: Using Loans and Credit to Make Purchases
Working with Installment Loans
An installment loanis a loan in which the principal and interest are paid back in installments. What makes the installment loan different from a conven- tional loan or promissory note is that the amount paid in each installment and the number of installments are what drive the interest rate. The interest may or may not be clearly indicated. The annual percentage rate,or APR, is the actual rate of interest charged for the privilege of having the loan. The stated rate and the actual rate are usually completely different things. For example, the stated rate may be 4%, but if you take into account the effect of monthly compounding, that rate is really 4.07415%. The difference may not seem like much, but it adds up when you’re dealing with lots of money. A for- mula allows you to determine the annual percentage rate. I introduce this for- mula in the following section.
Installment loans are commonly used when making purchases from retailers who are anxious to move their merchandise and earn a profit not only from the markup but also from the interest on the loan. You may be willing to pur- chase an item using an installment loan if your only option is to let that mer- chant be your banker. If you aren’t in the position to pay cash or borrow more money from a bank, the installment plan allows you the use of the mer- chandise immediately.
Calculating the annual percentage rate
The APR isn’t something that’s widely broadcast on many installment loan contracts; you’ll see the stated interest amount, but the APR takes a little more figuring. It takes into account the effects of compounding and any fees and extra charges. If you’ve ever tried to find a formula for determining APR, you’ve probably discovered that it’s difficult to find one. Most Web sites just want to do the calculations for you. It must be assumed that you really don’t want to tackle a formula or that it’s beyond your capabilities. Well, I know better than that! Of course you want to do the math!
The best formula I’ve found is a variation on Steve Slavin’s formula in Business Math(Wiley). Here it is:
APR P n
m
P n m Prt
n mrt 1
2
1 2
1 finance charge 2
= + =
+ =
^ + _
^
^ h
i
h h
where mis the number of payments made each year, Pis the principal or amount borrowed, ris the interest rate, tis the number of years involved, and nis the total number of payments to be made. After you determine your vari- ables, you’re all set to plug in and solve. Try out an example.
What’s the APR of a loan for $6,000 for 2 years at 10.125% interest with monthly payments?
The number of payments per year, m, is 12; the interest rate, r, is 10.125, or 0.10125; the amount of time, t, is 2; and the number of payments, n, is 2 ×12 = 24. Plugging these numbers into the formula for APR and solving gives you an answer:
.
. .
APR n mrt
1 2
24 1 2 12 0 10125 2
25
4 86 0 1944
= +
= +
= =
^ h^ h h^
The APR of 19.44% is much higher than the stated interest rate of 10.125%.
You don’t have any choice on the rate — the APR is what’s used in the com- putations. You just need to know what you’re getting into when you agree to a particular stated rate.
Making purchases using an installment plan
Making purchases with an installment plan allows you to make use of the item or items you’re purchasing while you’re paying for them. Making installment purchases is often a necessary part of doing business. For instance, you may need machinery or supplies to provide services or produce products. The profit from those services or products allows you to make the installment pay- ments. The trick is to be sure that you aren’t paying more than you intended for the machinery or supplies. The stated costs or payments may be decep- tive. You may think that you’re getting a good deal — until you do the math and determine that the total payback far exceeds the value of the item.
For example, an advertisement claiming that you can purchase a riding trac- tor for just $2,500 down and $200 each month for the next 5 years may seem like a great deal. But how good a deal is it? Read through the following exam- ple to find out.
So, say that you’re deciding whether to purchase a $10,000 riding tractor using an installment payment plan in which you put down $2,500 and pay
$200 each month for the next 5 years. What’s the APR on this plan?
175
Chapter 12: Using Loans and Credit to Make Purchases
You first need to determine the finance charge, because no interest rate is given. The total cost to you is the down payment of $2,500 plus 5 years of monthly payments of $200. So your cost is $2,500 + 5 ×12 ×$200 = $2,500 +
$12,000 = $14,500. You’ll end up paying $14,500 for a riding tractor that costs
$10,000 in cash. So the extra charge is $14,500 – $10,000 = $4,500.
Using the formula for APR, the number of payments per year, m, is 12. The principal, P, is $12,000 (the 5 years of payments), and the total number of payments, n, is 60. By plugging these numbers into the formula, you get
, ,
,
, .
APR P n
m
1 2
12 000 60 1 2 12 4 500
732 000 108 000
0 147541 finance charge
.
= +
= +
=
^ _
^
^ _
h i
h
h i
The interest rate comes out to be more than 14.75%.