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Compare financing options

Comparing financing options involves interpreting principal, down payment, interest rate, compounding or payment frequency, term, periodic payment, fees, and total amount repaid for standard fixed-rate loans or installment purchases. The learner reasons that a smaller periodic payment can produce a greater total cost when the term is longer and distinguishes an advertised interest rate from the overall financing cost, including fees, using equations, tables, and amortization schedules. Variable-rate loans, refinancing, tax effects, inflation adjustments, and advanced present-value models are outside this scope.

Detailed Explanation: Compare financing options

To compare financing options, do not look only at the periodic payment or advertised interest rate. Compare:

  • the amount borrowed, after the down payment;
  • the interest rate and payment frequency;
  • the number of payments;
  • fees;
  • the total amount paid.

A longer loan term often has a smaller payment but a greater total cost.

Example

A laptop costs 20{,}000.Youmakea. You make a $2{,}000$ down payment, so the amount financed is

P=20,000−2,000=$18,000.P=20{,}000-2{,}000=\$18{,}000.

You are comparing two fixed-rate loans. Both use monthly payments.

OptionAnnual interest rateTermFee
A6%6\%3 years200$
B5.5%5.5\%5 years0$

Step 1: Find the monthly rate and number of payments

For a monthly loan,

i=annual rate12andn=(years)(12).i=\frac{\text{annual rate}}{12} \qquad\text{and}\qquad n=(\text{years})(12).

For Option A,

i=0.0612=0.005,n=3(12)=36.i=\frac{0.06}{12}=0.005, \qquad n=3(12)=36.

For Option B,

i=0.05512=0.004583,n=5(12)=60.i=\frac{0.055}{12}=0.004583, \qquad n=5(12)=60.

Step 2: Calculate each monthly payment

For a standard fixed-rate loan, use

M=P(i1−(1+i)−n),M=P\left(\frac{i}{1-(1+i)^{-n}}\right),

where MM is the periodic payment.

For Option A,

MA=18,000(0.0051−(1.005)−36)≈$547.59.M_A =18{,}000\left(\frac{0.005}{1-(1.005)^{-36}}\right) \approx \$547.59.

For Option B,

MB=18,000(0.0045831−(1.004583)−60)≈$343.82.M_B =18{,}000\left(\frac{0.004583}{1-(1.004583)^{-60}}\right) \approx \$343.82.

Option B has the smaller monthly payment.

Step 3: Find the total of the loan payments

Multiply the payment by the number of payments.

For Option A,

36($547.59)≈$19,713.24.36(\$547.59)\approx \$19{,}713.24.

Adding the 200$ fee,

loan cost for A=$19,713.24+$200=$19,913.24.\text{loan cost for A} =\$19{,}713.24+\$200 =\$19{,}913.24.

For Option B,

60($343.82)≈$20,629.20.60(\$343.82)\approx \$20{,}629.20.

There is no fee, so

loan cost for B=$20,629.20.\text{loan cost for B}=\$20{,}629.20.

Step 4: Include the down payment

The total amount paid for the laptop is the down payment plus the loan cost.

OptionDown paymentPayments and feesTotal paid
A2{,}000$19{,}913.24$21{,}913.24$
B2{,}000$20{,}629.20$22{,}629.20$

Option A is cheaper overall by approximately

$22,629.20−$21,913.24=$715.96.\$22{,}629.20-\$21{,}913.24=\$715.96.

Although Option B advertises a lower interest rate and has a much smaller monthly payment, its five-year term means interest is charged for more months. Therefore, Option A is the better financing choice if the goal is to pay the least overall.

Learn by doing: Compare financing options

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    Financial Literacy - Interest and Fees - Compound Continual vs Discrete - Comparison to Better Option

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