calculating future value of retirement account in which you deposit $2,000 a year for 30 years with an annual interest rate of 7 percent?
Jenny intends to retire in 20 years. Upon retirement, she will require a yearly cash flow of $80,000 for
25 years to support her lifestyle (yearly cash flows assumed to occur at the end of each year).
Anticipating her retirement plan, she started investing $6,000 per year five years ago and will continue to do so for 20 more years. How much more will Jenny have to invest each year for the next 20 years to have the necessary funds for her retirement? Use a 10% per year discount rate throughout this problem (for discounting or compounding).
To calculate the future value of a retirement account, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
where:
FV = Future Value
P = Annual deposit amount
r = Annual interest rate
n = Number of years
In your case, the annual deposit amount (P) is $2,000, the annual interest rate (r) is 7 percent (0.07), and the number of years (n) is 30. Let's substitute these values into the formula:
FV = $2,000 * [(1 + 0.07)^30 - 1] / 0.07
Now, let's calculate the future value of the retirement account:
FV = $2,000 * (1.07^30 - 1) / 0.07
FV = $2,000 * (2.990578 - 1) / 0.07
FV = $2,000 * 1.990578 / 0.07
FV = $57,813.33
Therefore, the future value of the retirement account would be approximately $57,813.33 after 30 years of deposits with an annual interest rate of 7 percent.
To calculate the future value of a retirement account, you can use the formula for compound interest:
Future Value = P * (1 + r)^n
Where:
- P is the annual deposit amount ($2,000 in this case)
- r is the annual interest rate (7% or 0.07)
- n is the number of years (30 in this case)
Let's plug in the values and calculate:
Future Value = $2,000 * (1 + 0.07)^30
Now, let's break it down step by step:
1. Add 1 to the annual interest rate: 1 + 0.07 = 1.07
2. Raise this value to the power of the number of years: 1.07^30 ≈ 5.4277
3. Multiply this result by the annual deposit amount: $2,000 * 5.4277 ≈ $10,855.41
Therefore, the future value of the retirement account, after 30 years, with an annual deposit of $2,000 and an interest rate of 7%, is approximately $10,855.41.