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How to Calculate Present Values Using Timelines

In economy it’s important to talk about present values, as the value of money changes over time. $ $1$ is not worth the same today as $ $1$ will be worth in a year’s time. Inflation and the general economic development in the world affects the value of money. This is important to consider when you look at monetary values from different time periods.

Theory

Present Value

When we talk about present value, we are describing what future money would have been worth today.

Present values are often linked to loans in order to find the actual value of the loan, and has a quotient

k = \frac{1}{growth factor} = \frac{1}{{(1 + \frac{p}{100})}^{n}} .

The present value $K_{0}$ of a sum $K_{n}$ that will be paid back in $n$ periods of time is given as

K_{0} = \frac{K_{n}}{{(1 + \frac{p}{100})}^{n}},

where $p$ is the interest in percentages.

Example 1

You have decided to buy a car in 7 years, and you’re saving up money to do so. The car value of the car is $$ 30 000$ , and you get $3 %$ interest on the money. How much do you have to set aside today to have $$ 30 000$ in seven years?

You insert the numbers into the formula above and get

K_{0} = \frac{30 000}{{(1 + \frac{3}{100})}^{7}} = $ 24 392.75 .

That means that if you put $ $24 392.75$ in the bank today, you will have enough money to buy the $ $30 000$ car in seven years.

Loan

When looking at loans, it’s useful to draw a timeline. A timeline helps you remember how many periods the money is split across and how large the payments should be. Here’s an example concerning the present value of a loan:

Example 2

How much mortgage can you take? You’re able to pay $$ 800$ each month, and are set to make annual repayments. The interest is $5 %$ , and you pay the loan back over a period of 20 years, with the first payment being after one year.