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Why? Because you can use money to make more money! You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest. Example: You can get 10% interest on your money.So $1,000 now can earn $1,000 x 10% = $100 in a year. Your $1,000 now can become $1,100 in a year's time. Present Value We say the Present Value of $1,100 next year is $1,000 Because we could turn $1,000 into $1,100 (if we could earn 10% interest). Now let us extend this idea further into the future ... How to Calculate Future PaymentsLet us stay with 10% Interest. That means that money grows by 10% every year, like this: So:
In fact all those amounts are the same (considering when they occur and the 10% interest). Easier CalculationBut instead of "adding 10%" to each year it is easier to multiply by 1.10 (explained at Compound Interest): So we get this (same result as above): Future Back to NowAnd to see what money in the future is worth now, go backwards (dividing by 1.10 each year instead of multiplying): Example: Sam promises you $500 next year, what is the Present Value?To take a future payment backwards one year divide by 1.10 So $500 next year is $500 ÷ 1.10 = $454.55 now (to nearest cent). The Present Value is $454.55 Example: Alex promises you $900 in 3 years, what is the Present Value?To take a future payment backwards three years divide by 1.10 three times So $900 in 3 years is: $900 ÷ 1.10 ÷ 1.10 ÷ 1.10 $900 ÷ (1.10 × 1.10 × 1.10) $900 ÷ 1.331 $676.18 now (to nearest cent). Better With ExponentsBut instead of $900 ÷ (1.10 × 1.10 × 1.10) it is better to use exponents (the exponent says how many times to use the number in a multiplication). Example: (continued)The Present Value of $900 in 3 years (in one go): $900 ÷ 1.103 = $676.18 now (to nearest cent). As a formula it is: PV = FV / (1+r)n
Example: (continued)Use the formula to calculate Present Value of $900 in 3 years: PV = FV / (1+r)n PV = $900 / (1 + 0.10)3 = $900 / 1.103 = $676.18 (to nearest cent).
Let us use the formula a little more: Example: What is $570 next year worth now, at an interest rate of 10% ?PV = $570 / (1+0.10)1 = $570 / 1.10 = $518.18 (to nearest cent) But your choice of interest rate can change things! Example: What is $570 next year worth now, at an interest rate of 15% ?PV = $570 / (1+0.15)1 = $570 / 1.15 = $495.65 (to nearest cent) Or what if you don't get the money for 3 years Example: What is $570 in 3 years time worth now, at an interest rate of 10% ?PV = $570 / (1+0.10)3 = $570 / 1.331 = $428.25 (to nearest cent) One last example: Example: You are promised $800 in 10 years time. What is its Present Value at an interest rate of 6% ?PV = $800 / (1+0.06)10 = $800 / 1.7908... = $446.72 (to nearest cent) |