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How To Calculate The Future Value Of Money (An Investment) Explained - Time Value Of Money
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In this video we discuss how to calculate the future value of money, or an investment. We go through the formula for future value and show a few examples going through the calculations
Transcript/notes
The formula for calculating the future value of money is, future value equals, the present value, times the quantity, 1 plus r, divided by n raised to the n times t.
In this formula, present value represents the value today of an amount, r represents the yearly interest rate, n represents the number of compounding periods per year and t represents the time in years.
As an example, let’s say that someone invests $2000 in an account that pays 7.5% interest per year. The interest is compounded quarterly, so 4 times per year. What is the future value amount after 5 years?
Using the formula, we have future value equals, $2000, times the quantity, 1 plus .075, the decimal value of the yearly rate of 7.5%, divided by 4, the number of compounding periods per year, raised to 4, the number of compounding periods per year, times 5, the number of years.
.075 divided by 4 equals .01875, and 4 times 5 equals 20, and we have future value equals, $2000 times the quantity 1 plus .01875 raised to the 20. After the addition in the parenthesis, we have $2000 times 1.01875 raised to the 20. 1.01875 raised to the 20 equals 1.449948. Now we have $2000 times 1.449948, which equals $2899.90 rounded off.
So, the future value of $2000 at a yearly rate of 7.5%, compounded quarterly for 5 years is $2899.90.
And here are a couple of more examples on the screen for you of how to calculate the future value.
Chapters/Timestamps
0:00 Formula for future value of money
0:10 Definitions
0:22 Example problem for future value of money
1:30 More examples
Transcript/notes
The formula for calculating the future value of money is, future value equals, the present value, times the quantity, 1 plus r, divided by n raised to the n times t.
In this formula, present value represents the value today of an amount, r represents the yearly interest rate, n represents the number of compounding periods per year and t represents the time in years.
As an example, let’s say that someone invests $2000 in an account that pays 7.5% interest per year. The interest is compounded quarterly, so 4 times per year. What is the future value amount after 5 years?
Using the formula, we have future value equals, $2000, times the quantity, 1 plus .075, the decimal value of the yearly rate of 7.5%, divided by 4, the number of compounding periods per year, raised to 4, the number of compounding periods per year, times 5, the number of years.
.075 divided by 4 equals .01875, and 4 times 5 equals 20, and we have future value equals, $2000 times the quantity 1 plus .01875 raised to the 20. After the addition in the parenthesis, we have $2000 times 1.01875 raised to the 20. 1.01875 raised to the 20 equals 1.449948. Now we have $2000 times 1.449948, which equals $2899.90 rounded off.
So, the future value of $2000 at a yearly rate of 7.5%, compounded quarterly for 5 years is $2899.90.
And here are a couple of more examples on the screen for you of how to calculate the future value.
Chapters/Timestamps
0:00 Formula for future value of money
0:10 Definitions
0:22 Example problem for future value of money
1:30 More examples
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