C1T1L3 · Revised 2026-10-26

Decision and objectives

Practical task: Compare two reinvestment paths over one common horizon

Objectives: Compound a sequence of returns; Discount a future receipt using a matched convention; Annualize a historical period without implying a forecast.

Required prior knowledge: C1T1L2. Classification: domestic. Revision: 2026-10-26. All fictional names, prices, rates, fees, calendars and tax schedules below are hypothetical unless explicitly identified as a dated document observation.

A quoted annual rate, an observed monthly gain and a promised maturity amount are different inputs. Decide whether the task is to accumulate cash, compare present values or standardize historical reporting. Each has a different purpose. State the period, currency, day basis and reinvestment assumption before calculating. A percentage without a time interval cannot be compared responsibly.

Mechanics

Compounding earns subsequent returns on prior gains that remain invested. With no external cash flows, ending value is starting cash multiplied by each period's growth factor, (1 + r). Discounting reverses this process to express a future cash amount in today's units under a stated required return. A discount rate is an assumption about opportunity cost and risk; it does not become a contractual investment return because it appears in a spreadsheet.

If tax or fees are deducted between periods, only the remaining cash compounds. If gains are distributed and spent, the simple product of total returns requires an explicit reinvestment convention. Fund unit prices and a distributing security therefore need a consistent total-return basis.

Price and return drivers

For two periods, cumulative return = (1 + r1) × (1 + r2) − 1. Present value of a receipt at n matching periods = receipt / (1 + discount rate)^n. Historical annualization using a declared 365-day basis is (1 + observed return)^(365 / days) − 1. Positive elapsed days and a positive growth factor are required. Annualizing a short sample amplifies its noise and never demonstrates that its result is repeatable.

Worked case

Hypothetical TRY 100,000 earns 4% over the first month and 3% over the second, both after embedded fund expenses and before investor-level tax. Ending value = 100,000 × 1.04 × 1.03 = TRY 107,120; cumulative return is 7.12%, rather than 7%. Alternative B promises TRY 108,000 after the same two-month horizon. At a hypothetical required return of 3.5% per month, its present value is 108,000 / 1.035^2 = TRY 100,819.16. This present value is a decision aid, not an executable purchase quote.

A separate hypothetical 30-day historical gain of 3% annualizes to 1.03^(365/30) − 1 = approximately 43.28%. State “historical annualized equivalent”; do not say the product will earn that amount next year.

Adverse case

Change the second month to −5%. Ending value becomes 100,000 × 1.04 × 0.95 = TRY 98,800, a 1.2% loss. Averaging 4% and −5% gives −0.5% per month; multiplying that by two gives −1%, which misses compounding. The adverse path also invalidates an assumption that each monthly gain can be reinvested at the first month's attractive rate. A locked rate and a floating future reinvestment rate carry different risks.

Practical use

Obtain the contractual accrual convention for a bank product and the total-return definition for fund data. Do not insert “365” into a contract that uses another denominator. A common comparison can use a hypothetical standard basis for analysis, but contractual cash amounts must first be calculated correctly. Include investor charges and hypothetical tax at their actual assumed dates; embedded fund expenses must not be subtracted again. For an actual Turkish tax-net comparison, verify the income year, resident individual or entity status, instrument/acquisition date and applicable effective rule with GIB.

Decision boundaries

Compounding is useful when period returns are measured consistently and cash remains invested. Discounting is useful when timing differs, but a single rate can hide differences in credit or access. Annualization supports comparability; it cannot repair a very short or selectively chosen sample. Decline a “highest annualized return” decision when the spending horizon is short and the product's next redemption price is uncertain. Use the matched-horizon cash timeline as the final check.

Practice and references

Exercise: hypothetical TRY 80,000 earns +6% then −2% over two equal periods. A competitor pays TRY 84,000 after those periods. Calculate ending value, cumulative return and the competitor's present value at 2% per period. Answer: 80,000 × 1.06 × 0.98 = TRY 83,104, a 3.88% cumulative return. Competitor present value = 84,000 / 1.02^2 = TRY 80,738.18. Before choosing, compare credit, liquidity and tax on the same dates; the present-value advantage does not settle those issues.

Takeaway: match the rate's period to its cash flow and keep reporting arithmetic separate from prediction.

Reference guide: bank-deposit; mutual-fund; compound-return; annualized-return; present-value; compounding; annualized-return; discount-rate. Next: C1T1L4. Topic test.

Sources: SPK Mutual Funds Introduction Guide — What is a fund; fund expenses; fund types; founder and manager; recorded units; date not stated; retrieved 2026-10-26; checked 2026-10-26; GIB Investment Income Tax Guide, publication 584 — Introduction; income classification; income excluded from declaration; withholding and declaration sections; date 2026-02; checked 2026-10-26. Source records: sources.json. Check the cited rule dates and confirm current dealing terms before any transaction.

Shared reference guide