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, you will need to use the formula for future value of a series of deposits. The formula is as follows:
Future Value = P * ((1 + r)^n - 1) / r
Where:
P = Amount of each deposit made each year ($2,000 in this case)
r = Annual interest rate (7% or 0.07 as a decimal)
n = Number of years the deposits are made (30 years in this case)
Now let's plug the values into the formula and calculate the future value:
Future Value = 2000 * ((1 + 0.07)^30 - 1) / 0.07
Calculating the exponent:
(1 + 0.07)^30 = 5.4274909
Substituting the value back into the formula:
Future Value = 2000 * (5.4274909 - 1) / 0.07
Simplifying the calculation:
Future Value = 2000 * 4.4274909 / 0.07
Finally, calculating the future value:
Future Value = $125,685.59
Therefore, the future value of the retirement account, given the annual deposits of $2,000 for 30 years at an annual interest rate of 7 percent, will be approximately $125,685.59.