When you put money into a savings account in the bank, you receive interest after a period. The period can for example be half a year or a whole year.

Such a period is called a term.

Each time a term has passed, the interest is added to the capital. This process is called future value.

Example:

You put 1000 euros in the bank. You receive 4% interest every half year.

First term:

$$ Interest = \frac{1000 \cdot 4}{100} = 40\ euros $$

The capital is now \(1000 + 40 = 1040\ euros\).

Second term:

$$ 1040 \cdot (1+0.04) = 1081.60\ euros $$

This continues as long as the money stays in the bank.

Future Value

Future value is the amount on the account after a number of terms. The formula is:

$$ K = K_0 \cdot (1+r)^n $$

Where:

• \(K\) = future value
• \(K_0\) = initial capital
• \(r\) = interest rate as a decimal per term
• \(n\) = number of terms

Example:

You put 1000 euros in the bank at 4% per term. There are 10 terms over 5 years (2 per year).

$$ K = 1000 \cdot (1+0.04)^{10} $$

$$ K = 1000 \cdot 1.48024 \approx 1480\ euros $$

After 5 years there will be about 1480 euros in the account.

Summary

• A term is the period when interest is added.
• Future value means that the interest is added to the capital after each term.
• The future value is calculated with \(K = K_0 \cdot (1+r)^n\).