Simple interest practice: classroom loans
Eight I = Prt problems built around class loans: interest, weekly payments with rounding, finding the rate, comparing offers, and paying off early. Answer key included.
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Classroom economy · Math practice
Borrowing class money: simple interest
I = Prt. P is the amount borrowed. r is the interest rate per month, as a decimal. t is the time in months, and in our class one month = 4 weeks, so t = weeks ÷ 4. The total to repay is P + I. Weekly payments are the total ÷ number of weeks, rounded to the cent; the last payment fixes any rounding.
1. You borrow $20 at 8% per month for 4 weeks. Find the interest, the total to repay, and the weekly payment.
2. You borrow $25 at 8% per month for 2 weeks. Find t, the interest, and the weekly payment.
3. You borrow $50 at 6% per month for 8 weeks. Find the interest, the total, and the weekly payment.
4. You borrow $100 at 4% per month for 6 weeks. Find the total. The total doesn't split evenly into 6 payments. What are the first five payments, and what is the last one?
5. You borrow $75 at 5% per month for 4 weeks. Find the interest, the first three payments, and the last payment.
6. A 4-week loan of $60 charged $4.80 in interest. What was the monthly rate?
7. You need $50. Offer A: 6% per month for 4 weeks. Offer B: 4% per month for 8 weeks.
(a) Which costs less in interest? (b) Which has the smaller weekly payment? (c) You earn $25 a week and a payment can't be more than 40% of weekly pay. Which offers can you take?
8. You borrow $100 at 4% per month for 8 weeks and make 3 weekly payments on time. Then, exactly 3 weeks after borrowing, you pay the rest off. You owe interest only for the 3 weeks you had the loan. How much do you pay to finish, and how much interest did you save?
From the Cashroom Supply Closetcashroomapp.com
Answer key
Simple interest practice: answers
| # | Work | Answer |
|---|---|---|
| 1 | t = 4 ÷ 4 = 1 I = 20 × 0.08 × 1 = 1.60 21.60 ÷ 4 = 5.40 | Interest $1.60, total $21.60, payments $5.40 a week |
| 2 | t = 2 ÷ 4 = 0.5 I = 25 × 0.08 × 0.5 = 1.00 26.00 ÷ 2 = 13.00 | t = 0.5, interest $1.00, payments $13.00 a week |
| 3 | t = 8 ÷ 4 = 2 I = 50 × 0.06 × 2 = 6.00 56.00 ÷ 8 = 7.00 | Interest $6.00, total $56.00, payments $7.00 a week |
| 4 | t = 1.5; I = 100 × 0.04 × 1.5 = 6.00 106.00 ÷ 6 = 17.666... → 17.67 5 × 17.67 = 88.35 106.00 − 88.35 = 17.65 | Total $106.00; five payments of $17.67, last payment $17.65 |
| 5 | I = 75 × 0.05 × 1 = 3.75 78.75 ÷ 4 = 19.6875 → 19.69 3 × 19.69 = 59.07 78.75 − 59.07 = 19.68 | Interest $3.75; three payments of $19.69, last payment $19.68 |
| 6 | 4.80 = 60 × r × 1 r = 4.80 ÷ 60 = 0.08 | 8% per month |
| 7 | A: I = 50 × 0.06 × 1 = 3.00; 53.00 ÷ 4 = 13.25 B: I = 50 × 0.04 × 2 = 4.00; 54.00 ÷ 8 = 6.75 40% of 25 = 10.00 | (a) A costs less ($3.00 vs. $4.00), even with the higher rate. (b) B ($6.75 vs. $13.25). (c) Only B; A's $13.25 is over the $10.00 limit. |
| 8 | Full loan: I = 100 × 0.04 × 2 = 8.00; 108.00 ÷ 8 = 13.50 Paid so far: 3 × 13.50 = 40.50 3 weeks: I = 100 × 0.04 × 0.75 = 3.00 Owed: 103.00 − 40.50 = 62.50 Saved: 8.00 − 3.00 = 5.00 | Pay $62.50 to finish; saves $5.00 in interest |
Talk about #7: a lower rate isn't always the cheaper loan. Time matters as much as rate, and the cheapest loan may have a payment you can't afford.
From the Cashroom Supply Closetcashroomapp.com