Simple Interest: I = Prt

What is simple interest?

Simple interest is computed only on the original principal, never on previously earned interest. Over time it grows linearly, not exponentially.

The formula

$I = P \cdot r \cdot t$ $A = P + I = P(1 + rt)$

where $P$ = principal, $r$ = annual rate as a decimal, $t$ = time in years, $I$ = total interest, $A$ = total owed.

Step-by-step solution

Setup: $P = 5000$, $r = 0.08$, $t = 3$.

Step 1 — Plug into the interest formula: $I = 5000 \cdot 0.08 \cdot 3$

Step 2 — Compute: $I = 5000 \cdot 0.24 = \boxed{1200}$

Step 3 — Total owed at maturity: $A = P + I = 5000 + 1200 = 6200$

Comparison with compound interest (same rate, same time)

If the same loan compounded annually, $A = 5000 \cdot 1.08^3 = 5000 \cdot 1.259712 \approx 6298.56$, i.e. $98.56 more in interest. For longer terms or higher rates, the gap between simple and compound widens dramatically — compound rises as an exponential while simple rises as a straight line.

Where simple interest still shows up

• Short-term car loans and some personal loans
• Treasury bills (discount basis)
• Many auto-title and payday loans advertise "simple interest"
• Bond accrued-interest conventions within a coupon period
• Some bridging and construction loans

Most savings, mortgages, credit cards, and corporate bonds use compound interest.

Rearranged formulas

Solving $I = Prt$ for other quantities:

• $P = \dfrac{I}{rt}$ — principal from interest
• $r = \dfrac{I}{Pt}$ — rate
• $t = \dfrac{I}{Pr}$ — time

Each is just a single division once three of the four variables are known.

Common mistakes

• Using the percentage form instead of the decimal. $r$ must be $0.08$, not $8$. Using 8 gives $I = 120{,}000$ — wildly off.
• Mixing units. If $r$ is annual but $t$ is in months, convert first: $t_{\text{years}} = t_{\text{months}}/12$.
• Treating accrued interest as principal. Simple interest never adds prior interest to the base — that's what makes it simple (and what makes it grow slower than compound).

Try it in the visualization

Adjust the rate and term. A straight line shows simple-interest growth; an exponential curve shows compound growth; shaded area between them is the extra you'd pay (or earn) under compounding.