ACTL10001 Formula Sheet

Summary:

This formula sheet is a comprehensive compilation of financial and demographic equations and metrics, acting as a valuable resource for professionals, students, and enthusiasts in these fields. Starting with fundamental financial concepts, the sheet offers insights into the workings of simple and compound interest, allowing users to understand the accumulation of wealth or debt over time. It elucidates discount factors, which play a pivotal role in determining the present value of future amounts. The sheet also distinguishes between nominal rates, basic interest rates without considering inflation or compounding, and effective rates, which consider the compounding period. Furthermore, it elaborates on the intricate relationship between effective rates and the force of interest, a concept essential for advanced financial studies.

The sheet extensively covers annuities, breaking them down into various categories and subcategories. This includes annuities in arrears (or ordinary annuities) which are payments made at the end of each period, and annuities in advance, often referred to as annuities due, where payments are made at the beginning of the period. It sheds light on monthly annuities, a common occurrence in financial transactions, and highlights the complexities of annuities with fluctuating interest rates or inconsistent payments.

The intricacies of treasury notes and bonds, staples in the financial market, are also thoroughly explored. Users are provided with a detailed understanding of yields, particularly yield-to-maturity, a critical measure of the bond’s profitability over its entire life. It also delves into various methodologies for estimating bond yields.

Excerpt:

ACTL10001 Formula Sheet

Formula sheet
1. Simple interest
A = P + I = P × (1 + t × r)
2. Simple discount
A − P = D = A × d × t
3. Compound interest
A = P(1 + i)?

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Three possible cases for the price P:
If P = F; the bond is sold at par;
YTM = coupon rate
If P < F; the bond is sold at a discount;
YTM > coupon rate
If P > F; the bond is sold at a premium.
YTM < coupon rate

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