3. Practice Example

Let's practice the computation of future values with an additional example:

 

Example 2

Suppose you invest 50'000 in 1 year and 30'000 in 4 years. The interest rate is 6%. How much money will you have in the bank account in 10 years?

 

Using the equation from before, we can write:

 

\( FV_T = \sum_{t=0}^{T} C_t \times (1+R)^{(T-t)} \)

 

In our example, we have cash flows in 1 year (C1) and in 4 years (C4). Consequently, when we write out the above expression, we get:

  

\( FV_{10} = C_1 \times (1+R)^{(10-1)} + C_4 \times (1+R)^{(10-4)} \)

 

 C1 is 50'000, C4 is 30'000, the interest rate (R) is 6% and the overall investment horizon (T) is 10 years. Hence:

 

\( FV_{10} = 50'000 \times 1.06^9 + 30'000 \times 1.06^6 \)

 

\( FV_{10} = 84'473.95 + 42'555.57 = 127'029.52 \)