INSTALLMENT BUYING WALTER S. SORILLO

MAED – MATHEMATICSREPORTER

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Buying on an installment plan is usually referred to as deferred-payment or time-payment plan.

Installment-buying, thus refers to the type of purchase which requires the buyer to pay a down payment upon purchase, and to pay the remaining balance in several periodic payments within a specified time span.

The total sum paid through installment is usually higher than the regular cash price.

WHAT IS INSTALLMENTS-BUYING?

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Finance charge (FC) –

the interest charge.

FC = Total of all -- Amount

monthly payments financed

Installment loan –

A loan paid off in a series of equal periodic payments.

Payments include interest and principal.

Amount financed (AF) –

the amount actually borrowed.

AF = Cash price -- Down payment

Deferred payment price (DPP) –

the total of all monthly payments plus the down payment.

DPP = Total of all + Down

monthly payments payment

COST OF INSTALLMENT BUYING

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COST OF INSTALLMENT BUYING

Mary Wilson would like to buy a boat that cost $9,345. If she puts down $300 she can finance the balance for 60 months at 10.5% (monthly payment = $194.38). Calculate the amount financed, finance charge, and deferred payment price.

Amount financed = Cash price -- Down payment

Finance charge = Total of all -- Amount monthly payments financed

Deferred payment Price = Total of all + Down monthly payments payments

$9,045 = $9,345 -- $300

$2,617.80 = $11,662.80 -- $9,045 ($194.38 x 60)

$11,962.80 = $11,662.80 + $300

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ANNUAL PERCENTAGE RATE (APR)

Calculating APR rate by table

Finance charge x $100 = Table 14.1Amount financed lookup number

$2,617.80 x 100 = $28.94 $9,045

Between 10.25% -- 10.50%

Truth in

Lending Act

APR must be

accurate to

the nearest

1/4 of 1%

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# of Payments 10.00% 10.25% 10.50% 10.75% 11.00% 11.25% 11.50% 11.75% 12.00% 12.25% 12.50%

36 16.16 16.58 17.01 17.43 17.86 18.29 18.71 19.14 19.57 20.00 20.43

37 16.62 17.06 17.49 17.93 18.37 18.81 19.25 19.69 20.13 20.58 21.02

38 17.08 17.53 17.98 18.43 18.88 19.33 19.78 20.24 20.69 21.15 21.61

39 17.54 18.00 18.46 18.93 19.39 19.86 20.32 20.79 21.26 21.73 22.20

40 18.00 18.48 18.95 19.43 19.90 20.38 20.86 21.34 21.82 22.30 22.79

41 18.47 18.95 19.44 19.93 20.42 20.91 21.40 21.89 22.39 22.88 23.38

42 18.93 19.43 19.93 20.43 20.93 21.44 21.94 22.45 22.96 23.47 23.98

43 19.40 19.91 20.42 20.94 21.45 21.97 22.49 23.01 23.53 24.05 24.57

44 19.86 20.39 20.91 21.44 21.97 22.50 23.03 23.57 24.10 24.64 25.17

45 20.33 20.87 21.41 21.95 22.49 23.03 23.58 24.12 24.67 25.22 25.77

46 20.80 21.35 21.90 22.46 23.01 23.57 24.13 24.69 25.25 25.81 26.37

47 21.27 21.83 22.40 22.97 23.53 24.10 24.68 25.25 25.82 26.40 26.98

48 21.74 22.32 22.90 23.48 24.06 24.64 25.23 25.81 26.40 26.99 27.58

49 22.21 22.80 23.39 23.99 24.58 25.18 25.78 26.38 26.98 27.59 28.19

50 22.69 23.29 23.89 24.50 25.11 25.72 26.33 26.95 27.56 28.18 28.80

60 27.48 28.22 28.96 29.71 30.45 31.20 31.96 32.71 33.47 34.23 34.99

Annual percentage rate table per $100 (partial)

ANNUAL PERCENTAGE RATE TABLE PER $100 (TABLE 14.1)

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CALCULATING THE MONTHLY PAYMENT BY FORMULA

Finance charge + Amount financedNumber of payments of loan

The pickup truck advertisement below shows a $194.38 monthly payment. We can check this by formula and by

table lookup.

$2,617.80 + $9,04560

= $194.38

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Step 2. Look up the rate (10.5%) and the number of months (60). At the intersection is the table factor showing the monthly payment per $1,000 ($21.49).

Step 3. Multiply the quotient in Step 1 by the factor in Step 2.

9.045 x $21.49 = $194.38

CALCULATING THE MONTHLY PAYMENT BY TABLE

Step 1. Divide the loan amount by $1,000.

$9,045 = 9.045$1,000

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LOAN AMORTIZATION TABLE (TABLE 14.2)

(MONTHLY PAYMENT PER $1,000 TO PAY PRINCIPAL AND INTEREST ON INSTALLMENT LOAN)

(PARTIAL)

Terms inmonths 7.50% 8.00% 8.50% 9.00% 10.00% 10.50% 11.00% 11.50% 12.00%

6 170.34 170.58 170.83 171.2 171.56 171.81 172.05 172.3 172.5512 86.76 86.99 87.22 87.46 87.92 88.15 88.38 88.62 88.8518 58.9 59.15 59.37 59.6 60.06 60.29 60.52 60.75 60.9824 45 45.23 45.46 45.69 46.14 46.38 46.61 46.84 47.0730 36.66 36.89 37.12 37.35 37.81 38.04 38.28 38.51 38.7536 31.11 31.34 31.57 31.8 32.27 32.5 32.74 32.98 33.2142 27.15 27.38 27.62 27.85 28.32 28.55 28.79 29.03 29.2848 24.18 24.42 24.65 24.77 25.36 25.6 25.85 26.09 26.3354 21.88 22.12 22.36 22.59 23.07 23.32 23.56 23.81 24.0660 20.04 20.28 20.52 20.76 21.25 21.49 21.74 21.99 22.24

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Alteres, Priscilla S. et al. Mathematics of Investment. Manila: Rex Book Store.2004.

Alteres, Priscilla S. et al. Business Mathematics. Manila: Rex Book Store.2003.

Internet:

REFERENCES:

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