This document provides three examples of calculating future and present values of investments using compound interest formulas. The first two examples show calculating the future value after 7 years of an initial $4000 investment at 5.5% annual interest, with the second example compounding interest monthly rather than annually, resulting in a higher future value. The third example calculates the present value of an annuity worth $11,375 in 5 years at 6% interest per year.

1. Future Value of an
Investment

2. Future Value Formula
A = P(1+ r)
n
FV = PV (1+ r)
n
With compound interest you earn interest on your interest

3. Example 1
Calculate the future value of an investment of $4000 at
5.5%p.a compounding annually for 7 years.
FV = PV (1+ r)
PV = $4000
r = 0.055
n
n=7
FV = 4000(1+ 0.055)
= $5818.72
7
the future value of the investment is $5818.72

4. Example 2
Calculate the future value of an investment of $4000 at
5.5%p.a compounding monthly for 7 years.
FV = PV (1+ r)
PV = $4000
n
0.055
r=
= 0.004583
12
n = 7 × 12 = 84
FV = 4000(1+ 0.004583)
= $5873.29
84
the future value of the investment is $5873.29
WHY is this different to Example 1?

5. Example 3 of an annuity that has a future
Calculate the present value
value of $11375 after 5 years at 6%p.a Answer to the
nearest dollar
FV = PV (1+ r)
FV
∴ PV =
n
(1+ r)
FV = $11375
n
r = 0.06
n=5
11375
PV =
5
(1+ 0.06)
= $8500
the present value of the annuity is $8500