Financial Mathematics • Topic 5 of 6

Loans

A loan is money borrowed that must be repaid, usually with interest. For a simple one-period loan, the total repaid is the principal plus the interest charged: with simple interest, that is P + P × r × t. A $5,000 loan at 8% for one year costs 5000 × 0.08 = $400 in interest, so $5,400 is repaid. The amount of interest depends on the principal, the rate and the time. Watch for whether a question asks for the interest alone or the total repayment. The SAT keeps loan problems to clean rates and short terms so the focus stays on setting up principal, rate and time correctly.

A horizontal stacked bar showing a light-blue principal segment and a green interest segment together forming the total repaidLoan repaymentPrincipal $5,000Interest$400Total repaid $5,400Total repaid = principal + interest

✅ Solved examples

1. A $5,000 loan at 8% simple interest for 1 year. Total repaid?
Interest 5000 × 0.08 = 400; total 5,400.
2. A $2,000 loan at 10% for 1 year. Interest?
2000 × 0.10 = $200.
3. A $3,000 loan at 6% for 2 years. Interest?
3000 × 0.06 × 2 = $360.
4. A $1,000 loan at 12% for 1 year. Total repaid?
Interest 120; total $1,120.

✏️ Practice — try these, take hints as needed

1. A $4,000 loan at 5% for 1 year. Interest?
P × r × t.
4000 × 0.05.
—
$200.
2. A $6,000 loan at 10% for 1 year. Total repaid?
Interest 600.
Add principal.
—
$6,600.
3. A $2,500 loan at 8% for 2 years. Interest?
2500 × 0.08 × 2.
—
—
$400.
4. A $10,000 loan at 7% for 1 year. Total repaid?
Interest 700.
10000 + 700.
—
$10,700.
5. A $1,500 loan at 6% for 1 year. Interest?
1500 × 0.06.
—
—
$90.

📝 Topic test — 8 questions

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