ACTL10001 Chap.1 Simple Interest and Discount
Simple Interest and Discount
Simple interest fixes the interest base at the original principal, so growth is linear in both the quoted rate and the term. Simple discount instead calculates a price by deducting a charge from the maturity amount. The two conventions may display the same percentage while producing different economic yields because their bases differ.
The safest method starts with a two-date cashflow line, converts the term into the rate's time unit, labels the known amount as present or future, and only then selects an equation. This chapter also distinguishes a pricing quotation from an investor return, which becomes important for bank bills and other short dated instruments.
What this chapter covers
- 01
Principal, interest and accumulated amount
- 02
Time fractions on the stated year basis
- 03
Simple accumulation A = P(1 + rt)
- 04
Simple discount price P = A(1 - dt)
- 05
Present and maturity value direction checks
- 06
Investor yield versus discount quotation
- 07
Equivalent annual compound return
- 08
Rounding and unit labels
Worked example · free
A short dated investment
- 1Convert time to years: t = 140/365.
- 1Interest = 9,000 × 0.046 × 140/365 = $158.79.
- 1Amount = principal plus interest = $9,158.79.
Key terms
- Simple Interest
- Interest calculated on the unchanged opening principal throughout the term.
- Simple Discount
- A pricing convention that deducts a time based charge from the future maturity amount.
- Principal
- The amount invested or borrowed at the starting valuation date.
- Maturity Value
- The amount payable at the end of the stated term.
- Time Fraction
- The term expressed in the same time unit used by the quoted rate.
- Investment Yield
- The return measured against the actual capital committed by the investor.
Simple Interest and Discount FAQ
When should I use simple interest?
Use it when the contract or question explicitly states a simple interest convention. Do not replace compound growth with simple interest merely because the term is short.
Why is a discount rate not the same as a yield?
The discount charge is measured against the maturity amount, while investment yield is measured against the smaller price paid today. Their numerical percentages therefore differ.
How do I handle a term in days?
Use the day count basis stated in the question, such as 365 days, and write the fraction explicitly before applying the annual rate to the stated principal.
What is the best error check?
At a positive rate, an accumulated amount should exceed principal and a discounted price should be below maturity value. Check those directions before accepting the result.
How can I distinguish a price quote from an earned return?
Identify the base used by the percentage. A simple discount quote applies to the maturity amount, while an investor yield measures the gain against the price actually paid. Translate both offers to cash amounts at common dates before comparing them.
Which details should appear in a complete short-term valuation answer?
Show the known cash amount on its date, the time fraction on the stated day-count basis, the percentage base and the equation used. Report both interest or discount and the resulting amount when relevant, retain precision until the last step, and add a direction check explaining why the later amount is larger or the earlier price is smaller.
A final label should identify dollars and the rate convention so the result can be interpreted without reconstructing the question. Preserve the original contractual quote alongside any converted comparison rate.
Exam move
Practise each problem with a two point timeline. Mark present and future amounts, state the day or month conversion, and name the base on which the percentage applies. After computing, translate the result into a sentence about the investor or borrower.
Mix direct accumulation, reverse principal problems, simple discount prices and yield translations so that formula choice follows the contract language rather than the position of the unknown. Begin a revision set with direct accumulation, then reverse the same facts to solve for principal, rate and term. This reveals which algebraic moves preserve the model and which accidentally change the interest base.
Include day-count questions on different stated year bases, writing the fraction before the decimal so the unit decision remains visible. Pair each simple-interest problem with a simple-discount version using the same maturity amount and horizon. Compare prices, dollar gains and investor yields rather than comparing quoted percentages.
For every answer, use a direction sentence: accumulation should raise value, discounting should lower a future payment, and the yield on a discounted price should exceed the numerically equal discount quote. Keep full precision through time fractions and rate conversions, then round money only at the reporting step. Build one short table that records contract wording, percentage base, equation and stakeholder perspective.
When a question presents two offers, choose a single comparison date and state whether the buyer or seller is making the decision. Finish the set by explaining why the simple model does not compound interim interest. That explanation checks conceptual understanding without relying on calculator output.
Rework any error by redrawing the cashflow line before changing the arithmetic, because most mistakes here begin with a mislabelled date or base.
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