3.6 Time Diagrams
The time diagram, or time line, graphically represents the time value of money.
The time diagram (Figure 3.6.1) is also called the time line . It is used to graphically represent the time value of money.
Although this diagram seems very simple and almost trivial at this point in the course, it is very important that you learn the basics here, and that you include the diagram in all problem solutions that involve cashflow.
Example 3.6.1
Calculate the maturity value of a 6-month loan of $5,000 at 8.25% simple interest.
[latex]P=$5,000;\; r= 8.25%=0.085;\; t=\frac{6}{12} years=0.5\; years[/latex]
Therefore:
[latex]FV=$5,000 (1+0.085\times 0.5)=$5,206.25[/latex]
Example 3.6.2
Calculate the maturity value of a $4,200 deposit made at a simple interest rate of 6.75% pa from March 3, 2001 to November 9, 2001.
[latex]t =\frac{313 - 62}{365}=\frac{251}{365}\; years[/latex] (from table 3.1)
OR
Using the Calculator:
DT1 = 3.0301 [ENTER]
↓DT2 = 11.0901 [ENTER]
↓[CPT] DBD = 251
[latex]P= $4,200;\; r = 6.75%= 0.0675[/latex]
Therefore:
[latex]FV =$4,200 \left(1 + 0.0675\times\frac{251}{365}\right)=$4394.95[/latex]
Knowledge Check 3.2
Now try these examples (be sure to draw the time diagrams).
- How much would have to be repaid if you borrowed $4,000 for 210 days at 8% simple interest?
- Calculate the maturity value of $1,250 which was invested from March 10, 2022 to September 8, 2022 at 6.75% simple interest.
- Joan Smith borrowed $2,500 from her father to start the school term. If she agreed to fully repay him the amount borrowed plus interest to be calculated at 3.75% simple, how much would she have to repay in exactly two years?
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