Theory of Interest 142

Visual Study Wall & Procedural Guide

Weekly Roadmap
Core Formulas
Calculator Hub
Week 1: Introduction to Interest
20-24 Jul
TB: 1.1 - 1.3.1 AF 1
Understanding the time value of money, simple interest, and basic compound interest concepts.
PV, FV, i, n
FV = PV(1 + i)ⁿ
Week 2: Compound Interest & Discounting
27-31 Jul
TB: 1.3.2 - 1.4 AF 2 | Tut 1
Moving money backward in time (discounting) and working with nominal vs. effective rates.
PV = FV(1 + i)⁻ⁿ
Week 3: Continuous Compounding
03-07 Aug
TB: 1.5 - 1.6 AF 3 | Tut 2
Force of interest and setting up equations of value for complex timelines.
FV = PV × e^(rn)
Week 4: Basic Annuities
10-14 Aug
TB: 1.7 AF 4 | Tut 3
Annuities-immediate (end of period) and annuities-due (beginning of period).
PV = PMT × a_n|i
Trap: Ask “when is the first payment?” before selecting a formula. Beginning-of-period payments need annuity-due logic or BEG mode on the calculator.
Week 5 & 6: General Annuities
17-28 Aug
TB: 2.1 - 2.3 AF 5, 6 | Tut 4, 5
When payment frequency does not match compounding frequency.
Trap: Do not simply change P/YR to match the payment frequency. First convert the rate to the correct period, then set up the annuity.
Week 7: Deferred & Increasing Annuities
31-04 Aug/Sept
TB: 2.4 AF 7 | Tut 6
Annuities that start later or grow arithmetically/geometrically.
Trap: Draw the timeline. The annuity value is normally one period before the first payment; you must then move it to the required focal date.
Mid-Semester Break (09-13 Sept)
Week 8: Perpetuities
14-18 Sept
TB: 2.5 AF 8 | Tut 7
Annuities that continue forever.
PV = PMT / i
Trap: This form assumes the first payment is one interest period from the valuation date. Shift the value on the timeline if it starts immediately.
A1 Assessment
22 Sept
Covers up to Section 2.5
Week 9 & 10: Loan Redemption
21-02 Sept/Oct
TB: 3.1 - 3.5 AF 9, 10 | Tut 8, 9
Amortization schedules, outstanding balances, and splitting payments into interest and capital.
Trap: Keep the original loan value, payment amount, rate, and number of payments consistent before calculating balances.
Week 11: Sinking Funds
05-09 Oct
TB: 2.6, 2.7 AF 11 | Tut 10
Alternative loan repayment where capital is accumulated in a separate fund.
Week 12: Valuation of Securities
12-16 Oct
TB: 4.1 AF 12 | Tut 11
Pricing bonds based on coupon payments and redemption value.
Trap: Do not value only the coupon stream. The redemption value is a separate cash flow at maturity and must also be discounted.
A2 & A3 Assessments
12 Nov & 05 Dec
Covers all course work

Hover or tap a card to reveal the formula.

📈

Simple Interest

Single period growth

I = P i t
Use when interest is calculated only on the original principal over the relevant time fraction.
🔄

Compound Interest

Multi-period growth

S = P(1 + i)ⁿ
Move a single amount forward through n equal interest periods.
⏪

Discounting

Moving backward

P = S(1 + i)⁻ⁿ
Move a single future amount back to its present value.
🔀

Nominal ↔ Effective

Rate conversion

i = (1 + i⁽ᵐ⁾/m)ᵐ − 1
Convert a nominal rate to an annual effective rate, or reverse it.
♾️

Continuous Compounding

Force of interest

S = P eʳᵗ
Use only when specified as a force of interest or continuous compounding.
📅

Annuity-Immediate

End of period

PV = PMT × aₙ|ᵢ
For equal payments at the end of each period.
⏮️

Annuity-Due

Beginning of period

äₙ|ᵢ = (1 + i)aₙ|ᵢ
For payments at the beginning of each period.
⏳

Perpetuity

Forever

PV = PMT / i
Level payment stream continuing indefinitely.
🏛️

Security Valuation

Bonds

P = PV(cpns) + PV(redemp)
Discount every coupon and the final redemption value to the focal date.

🧭 Which tool do I use?

1
Start with the timeline. One amount moving? Use single-sum accumulation/discounting.
2
Repeated payments? Level, increasing, deferred, or perpetual? Identifies the annuity type.
3
Frequencies differ? Convert the rate first using EFF% and NOM%.
4
TVM solvable? Use N, I/YR, PV, PMT, FV. Check cash-flow signs first!
5
Loan balance? Find payment, then use AMORT.
Sign Convention Rule: Outflows (money leaving) = Negative. Inflows (money arriving) = Positive. If PV is positive, PMT/FV must be negative.

Basic Setup & Clear

Clear memory and set 1 period/year.

■ C ALL
1 ■ P/YR

Set Decimals

Show 4 decimal places.

■ DISP 4

Nominal to Effective

15% comp. monthly → annual effective.

12 ■ P/YR
15 ■ NOM%
■ EFF%

Effective to Nominal

17.5% effective → comp. quarterly.

4 ■ P/YR
17.5 ■ EFF%
■ NOM%

Annuity Due (BEGIN)

Toggle for beginning-of-period payments.

■ BEG/END

Amortization

Interest & principal for payments 1 to 12.

1 INPUT 12
■ AMORT
= (PRIN) = (INT) = (BAL)