Computing future value. Calculate the future value of a retirement account in which you deposit 2,000 a year for 30 years with an annual interest rate of 7 percent.
To calculate the future value of a retirement account with regular deposits, you can use the compound interest formula. The formula is:
FV = P * (1 + r)^n - 1 / r
where:
FV is the future value of the retirement account
P is the annual deposit amount
r is the annual interest rate (as a decimal)
n is the number of years
In this case, you have an annual deposit of $2,000, a 7 percent annual interest rate, and a time period of 30 years. Let's substitute these values into the formula and calculate the future value.
First, convert the annual interest rate into a decimal by dividing it by 100. In this case, 7 percent becomes 0.07.
Now, substitute the values into the formula:
FV = $2,000 * (1 + 0.07)^30 - 1 / 0.07
Calculating the brackets part first:
FV = $2,000 * (1.07)^30 - 1 / 0.07
Now, calculate the power inside the brackets:
FV = $2,000 * (2.913)^30 - 1 / 0.07
Next, calculate the brackets part:
FV = $2,000 * 161.051 - 1 / 0.07
Subtract 1 from the brackets part:
FV = $2,000 * 160.051 / 0.07
Divide the result by the interest rate:
FV = $2,000 * 2286.44
Finally, calculate the future value:
FV = $4,572,880
So, the future value of the retirement account, after 30 years with a $2,000 annual deposit and a 7 percent annual interest rate, is $4,572,880.