Question: An item sells for $\usd{}4\,500$. Under hire purchase, you pay a $\usd{}1\,000$ deposit and repay the balance over $2$ years in monthly instalments, with simple interest of $7\%$ per annum on the balance. Find the monthly instalment and the total hire-purchase price.

Step 1. Interest is charged only on what you borrow:

Step 2. Simple interest on that balance:

Step 3. Total owed to the shop after the deposit, spread over $2 \times 12 = 24$ months:

Step 4. Total hire-purchase price = deposit + everything repaid:

— which is $\usd{}490$ more than the cash price, exactly the interest. ✓

⚠ Watch out: Interest applies to the balance after deposit, never the full price — $\frac{4500 \times 7 \times 2}{100}$ overcharges. And the instalment divides by the number of months (24), not years; quoting $\usd{}1\,995$ per "instalment" means the time unit got lost.

Question: A car's cash price is $\usd{}90\,000$. Shirley paid a down payment of $20\%$ and borrowed the rest at simple interest of $y\%$ per annum, repaying $\usd{}750$ monthly for $120$ months. Find the down payment, the total interest, and the value of $y$.

Step 1. Down payment:

Step 2. Total actually repaid to the bank:

Step 3. Interest = repaid − borrowed:

Step 4. Back-solve the rate with $T = 120$ months $= 10$ years:

⚠ Watch out: Two different $\usd{}90\,000$s appear — the cash price and the coincidental total of instalments; keep them apart, the interest comes from comparing instalments with the loan, not the price. And convert $120$ months to $10$ years before it enters $\frac{PRT}{100}$: rate per annum needs time in years.