Comparing Loans in Money Management - Grade 3

Learn about comparing loans with 5 detailed exercises on money management for 3rd grade math students.

Loan Comparison: Exercises 1 to 3
1 Interest Rate Comparison
Exercise 1
Your family needs to borrow $100. Bank A offers a loan with 5% interest. Bank B offers a loan with 8% interest. Which loan costs less?
Definition:

Interest rate: The extra money you pay back on top of the borrowed amount

Comparison method:
  1. Identify the loan amount (principal)
  2. Compare interest rates
  3. Calculate total repayment for each loan
  4. Choose the loan with lower total cost
Loan Amount
$100
Bank A
5%
Bank B
8%
Step 1: Calculate interest for Bank A

5% of $100 = $5

Step 2: Calculate total repayment for Bank A

$100 + $5 = $105

Step 3: Calculate interest for Bank B

8% of $100 = $8

Step 4: Calculate total repayment for Bank B

$100 + $8 = $108

Step 5: Compare total costs

$105 (Bank A) < $108 (Bank B)

Bank A costs less: $105 vs $108
Final answer:

Bank A's loan costs less with a total repayment of $105 compared to Bank B's $108.

Applied rules:

• Lower interest rate: Always results in lower total cost

• Percentage calculation: Multiply principal by interest rate

• Total cost: Principal + Interest = Total Repayment

2 Repayment Period Comparison
Exercise 2
You want to borrow $50. Loan Option 1: Pay back in 6 months. Loan Option 2: Pay back in 12 months. Which option has smaller monthly payments?
Definition:

Repayment period: How long you have to pay back the loan

Loan Amount
$50
Option 1
6 months
Option 2
12 months
Step 1: Calculate monthly payment for Option 1

$50 ÷ 6 months = $8.33 per month

Step 2: Calculate monthly payment for Option 2

$50 ÷ 12 months = $4.17 per month

Step 3: Compare monthly payments

$4.17 < $8.33

Step 4: Consider total cost (with same interest)

Longer periods usually mean higher total interest

Option 2 has smaller monthly payments: $4.17 vs $8.33
Final answer:

Option 2 (12 months) has smaller monthly payments of $4.17 compared to $8.33 for 6 months.

Applied rules:

• Monthly payment: Principal ÷ Number of months

• Payment flexibility: Longer periods = smaller monthly payments

• Interest consideration: Longer periods may increase total interest

3 Total Cost Comparison
Exercise 3
Compare two loans for $200: Loan A has 4% interest over 1 year. Loan B has 6% interest over 1 year. Which loan costs more in total?
Definition:

Total cost: The original loan amount plus all interest charges

Principal
$200
Loan A
4% interest
Loan B
6% interest
Step 1: Calculate interest for Loan A

4% of $200 = $8

Step 2: Calculate total cost for Loan A

$200 + $8 = $208

Step 3: Calculate interest for Loan B

6% of $200 = $12

Step 4: Calculate total cost for Loan B

$200 + $12 = $212

Step 5: Compare total costs

$212 (Loan B) > $208 (Loan A)

Loan B costs more: $212 vs $208
Final answer:

Loan B costs more with a total of $212 compared to Loan A's $208.

Applied rules:

• Total cost calculation: Principal + (Principal × Interest Rate)

• Comparison principle: Higher interest rate = Higher total cost

• Cost evaluation: Always compare final amounts

Loan Comparison Concepts
Total Repayment = Principal + Interest
Loan Calculation Formula
📊
Interest Rate
📅
Time Period
💰
Monthly Payment
📈
Total Cost
Feature Loan A Loan B
Principal $100 $100
Interest Rate 5% 8%
Time Period 1 year 1 year
Total Cost $105 $108
Low Rate
Less interest
Lower cost
Short Term
Higher payments
Less interest
Long Term
Lower payments
More interest
Loan Comparison Rule: Always compare interest rates, time periods, and total costs.
Financial Principle: Lower interest rate usually means lower total cost.
Loan Comparison: Exercises 4 to 5
4 Combined Comparison
Exercise 4
Compare two loans for $300: Loan C has 3% interest over 6 months. Loan D has 5% interest over 12 months. Which loan has lower monthly payments? Which costs less overall?
Definition:

Combined comparison: Looking at multiple loan features together

Loan C
3% for 6m
Loan D
5% for 12m
Principal
$300
Step 1: Calculate interest for Loan C

3% of $300 = $9

Step 2: Calculate total for Loan C

$300 + $9 = $309

Step 3: Calculate monthly payment for Loan C

$309 ÷ 6 = $51.50 per month

Step 4: Calculate interest for Loan D

5% of $300 = $15

Step 5: Calculate total for Loan D

$300 + $15 = $315

Step 6: Calculate monthly payment for Loan D

$315 ÷ 12 = $26.25 per month

Step 7: Compare monthly payments

Loan D: $26.25 < Loan C: $51.50

Step 8: Compare total costs

Loan C: $309 < Loan D: $315

Loan D has lower monthly payments ($26.25 vs $51.50), but Loan C costs less overall ($309 vs $315)
Final answer:

Loan D has lower monthly payments ($26.25) but costs more overall ($315). Loan C costs less overall ($309) but has higher monthly payments ($51.50).

Applied rules:

• Trade-off principle: Lower monthly payments often mean higher total cost

• Separate calculations: Calculate monthly payments and total costs separately

• Decision making: Choose based on budget constraints vs total cost

5 Multiple Option Comparison
Exercise 5
You need $150. Compare three loan options: A ($155 total, 3 months), B ($160 total, 6 months), C ($165 total, 12 months). Which has the lowest monthly payment? Which has the lowest total cost?
Definition:

Multiple option comparison: Evaluating several loan options simultaneously

Option A
$155, 3m
Option B
$160, 6m
Option C
$165, 12m
Step 1: Calculate monthly payment for Option A

$155 ÷ 3 = $51.67 per month

Step 2: Calculate monthly payment for Option B

$160 ÷ 6 = $26.67 per month

Step 3: Calculate monthly payment for Option C

$165 ÷ 12 = $13.75 per month

Step 4: Compare monthly payments

Option C: $13.75 < Option B: $26.67 < Option A: $51.67

Step 5: Compare total costs

Option A: $155 < Option B: $160 < Option C: $165

Step 6: Determine lowest monthly payment

Option C has the lowest monthly payment

Step 7: Determine lowest total cost

Option A has the lowest total cost

Option C has lowest monthly payment ($13.75), Option A has lowest total cost ($155)
Final answer:

Option C has the lowest monthly payment ($13.75) but Option A has the lowest total cost ($155).

Applied rules:

• Systematic comparison: Calculate all metrics for each option

• Multiple criteria: Consider both monthly payment and total cost

• Trade-off analysis: Balance short-term vs long-term costs

Loan Comparison Guide: Understanding Key Features
Monthly Payment = Total Amount ÷ Number of Months
Payment Calculation
Key definitions:

Principal: The original amount borrowed

Interest rate: The percentage charged on top of the principal

Repayment period: How long you have to pay back the loan

Monthly payment: How much you pay each month

Total cost: The principal plus all interest charges

Loan Comparison Process:
  1. Identify: Find all loan options available
  2. Compare: Look at interest rates across all options
  3. Calculate: Determine monthly payments for each option
  4. Calculate: Determine total repayment for each option
  5. Decide: Choose based on your priorities (monthly payment vs total cost)
Tip 1: Always compare interest rates first - lower is better.
Tip 2: Calculate monthly payments to see if they fit your budget.
Tip 3: Don't forget to compare total repayment amounts.
Tip 4: Longer repayment periods mean smaller monthly payments but higher total costs.
Key comparison factors: Interest rate, repayment period, monthly payment, total cost.
Important considerations: Your ability to make monthly payments, total interest paid.
Loan Comparison Rules:

• Lower interest rate = Lower total cost (all else being equal)

• Shorter repayment period = Higher monthly payments but lower total interest

• Longer repayment period = Lower monthly payments but higher total interest

• Always calculate both monthly payment and total cost

• Choose based on your financial situation and priorities

Questions & Answers

Question: Why is it important to compare loans? Isn't borrowing money the same no matter where you get it?

Answer: Great question! Borrowing money is NOT the same everywhere. Different lenders charge different interest rates, which means you pay different amounts back. Think of it like buying the same toy at different stores - one store might sell it for $10 and another for $12.

For example, if you borrow $100:

  • At 5% interest, you'd pay back $105
  • At 10% interest, you'd pay back $110

By comparing loans, you can save money by choosing the one with the lowest interest rate and best terms for your situation.

Question: How can I help my child understand the concept of interest when comparing loans?

Answer: Use simple analogies that children can relate to:

  • The "Borrowing" Analogy: "If you borrow a toy from a friend and promise to give them a small treat in return, that treat is like interest."
  • The "Renting" Analogy: "When you rent a video game, you pay extra to use it temporarily. Interest is like renting money."
  • The "Extra Fee" Concept: "It's like paying a small fee for the privilege of having money before you earn it."

Use concrete examples with small amounts: "If you borrow $10 and have to pay back $11, the extra $1 is interest."

Question: How do I explain the trade-off between monthly payments and total cost to young students?

Answer: Use simple scenarios that children understand:

The Ice Cream Example: "Imagine you want an ice cream that costs $6. You can either:

  • Pay $2 each day for 3 days (higher daily cost, lower total time)
  • Pay $1 each day for 6 days (lower daily cost, higher total time)

The Piggy Bank Analogy: "If you save money slowly over time, you need to save for longer, but each day's savings can be smaller. If you save quickly, you save for less time but need more money each day."

Explain that with loans, spreading payments over more months makes each payment smaller, but you end up paying more in total because of interest accumulating over time.