These questions ask you to calculate or compare simple interest and repeated percentage growth. The decisive clue is whether each period uses the original amount again or uses the amount reached at the end of the previous period.
Identify the base for each period
Start by naming the initial amount P, the rate p% per period and the number of periods n. If the wording says simple interest, calculate one period's interest as P × p/100. That same amount is added in every period, so total interest is P × p/100 × n. Add P only if the final total is requested.
For example, 700 dollars at 3% simple interest for four years earns 700 × 0.03 = 21 dollars each year. The interest is 21 × 4 = 84 dollars, and the final total is 700 + 84 = 784 dollars. Notice that the yearly addition remains fixed because its base remains 700 dollars.
If the wording says an amount grows by p% each period, use repeated growth. Form the multiplier 1 + p/100 and apply it n times, always to the latest amount. A quantity of 300 growing by 6% for two periods becomes 300 × 1.06 × 1.06 = 337.08. The second increase is larger than the first because it includes growth on the earlier increase.
| Mechanism | Calculation |
|---|---|
| Simple interest earned | P × p/100 × n |
| Final total with simple interest | P + P × p/100 × n |
| Repeated growth for n periods | P × (1 + p/100), with the multiplier applied n times |
Both mechanisms give the same total after one period because each first increase is p% of P. After more than one positive-growth period, repeated growth is larger: simple interest keeps adding a fixed amount, while repeated growth earns a percentage of earlier increases too.
Common traps
| Tempting route | How to reject it |
|---|---|
| Adding the principal when only the interest is requested | Read the requested quantity before the final step. Interest excludes the starting principal; a final total includes it. |
| Giving one period's interest for a multi-period question | The first calculation gives the fixed yearly amount only. For simple interest, multiply it by the stated number of periods. |
| Applying a growth multiplier repeatedly to simple interest | Simple interest never moves its base away from the original principal. Repeated multiplication belongs only when the amount grows from its updated value. |
| Adding the same percentage of the original amount during repeated growth | That turns growth into a fixed addition. Recalculate each period from the current amount by applying the multiplier again. |
| Assuming the mechanisms differ immediately or remain equal for several periods | They match after the first period. From the second positive-growth period onwards, only repeated growth includes growth on an earlier increase. |
Try it
An account holds 1200 dollars at 4% simple interest per year for 3 years. What is the final total? Enter the amount in dollars.
A bacteria culture starts with 500 cells and grows by 10% each hour for 2 hours. Enter the final number of cells.
A 900 dollar bond pays 7% simple interest per year for 4 years. How much interest is earned in total? Enter the amount in dollars.