3.5 Calculating the Future Value  

The future value (or maturity value) is the total amount due at the end of a loan and is calculated by adding the interest due to the original principal.

[latex]FV=P+I[/latex]

Example 3.5.1

1. If $9,600 is borrowed and $800 interest is due, what is the future value (maturity value) of the loan?

• P = $9,600
• I = $800
• FV = $9,600 + $800 = $10,400

2. Calculate the future value (maturity value) of a $6,500 loan at 8.5% (per annum or pa) simple if the loan was taken out on February 12, 2023 and repaid on August 15, 2023.

First we count the days:

Using the Calculator:

DT1 = 2.1223 [ENTER]
↓DT2 = 8.1523 [ENTER]
↓[CPT] DBD = 184

Using Table 3-1:

[latex]t=\frac{227-43}{365}=\frac{184}{365} years[/latex]

Therefore,

[latex]I=Prt=$6,500 \times 0.085\times\frac{184}{365}=$278.52[/latex]

And

[latex]FV=P+I=$6,500+$278.52=$6,778.52[/latex]

You can simplify the Future Value equation as follows:

Since [latex]I = Prt[/latex] and [latex]FV = P + I[/latex]

now, substitute for I. Therefore,

[latex]FV = P + (Prt)[/latex]

Factoring out the P, you get

[latex]FV = P(1+rt)[/latex]

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