Financial Timelines and Changing Rates

Financial Timelines and Changing Rates

A financial timeline places cash flows at their correct dates and applies each interest or depreciation factor for the correct number of periods. When rates change, split the timeline into stages rather than forcing one rate across the entire period. State whether a payment happens at the beginning or end of a period; timing changes the exponent.

Worked reasoning

R10 000 grows at 8% for 2 years then 10% for 1 year: $10000(1.08)^2(1.10)=\text{R}12\,830.40$.

Exam method

1. Mark time zero and each rate change. 2. Write one factor per timeline segment. 3. Multiply factors in chronological order and attach the final date/value.

Time zero is a decision

Put deposits, withdrawals and rate changes precisely at the correct tick on the timeline. A payment at the start of a year receives one more period of interest than an end-of-year payment. Read the wording for ‘at the end of each year’ versus ‘immediately’. In a changing-rate question, multiply one factor for each arrow; this prevents both overcounting and undercounting periods. The timeline is also an excellent checking tool after algebra is complete.

One-minute retrieval: Financial Timelines and Changing Rates

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.