You annually invest $1,500 in an individual retirement account starting at the age of 20 and make the contributions for 10 years. Your twin sister does the same starting at age 30 and makes the contributions for 30 years. Both of you earn 7 percent annually on your investment. Who has the larger amount at age 60?
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You annually invest $1,500 in an individual retirement account (IRA) starting at the age of 20 and make the contributions for 10 years. Your twin sister does the same starting at age 30 and makes contributions for 30 years. Both of you earn 7 percent annually on your investment. Who has the larger amount at age 60?
To determine who has the larger amount at age 60, we can calculate the future value of investments for both scenarios.
For your investment:
- You invest $1,500 annually for 10 years, starting at age 20.
- The interest rate is 7 percent.
Using the formula for the future value of an ordinary annuity, the calculation is as follows:
Future Value = P * [(1 + r)^n - 1] / r
Where:
P = Annual investment amount
r = Interest rate per compounding period
n = Number of compounding periods
In this case,
P = $1,500
r = 7% or 0.07
n = 40 (Age 60 - Age 20)
Future Value = $1,500 * [(1 + 0.07)^40 - 1] / 0.07
Future Value ≈ $348,438.67
For your twin sister's investment:
- She invests $1,500 annually for 30 years, starting at age 30.
- The interest rate is 7 percent.
Using the same formula:
P = $1,500
r = 7% or 0.07
n = 30 (Age 60 - Age 30)
Future Value = $1,500 * [(1 + 0.07)^30 - 1] / 0.07
Future Value ≈ $447,712.79
Therefore, your twin sister will have the larger amount at age 60 with approximately $447,712.79, compared to your approximately $348,438.67.
To determine who has the larger amount at age 60, we need to calculate the future value of the investments for both you and your twin sister.
First, let's calculate the future value of your investment. Since you contribute $1,500 annually for 10 years and earn 7 percent annually, we can use the future value of an ordinary annuity formula:
Future Value = Payment x ((1 + interest rate)^(number of periods) - 1) / interest rate
Plugging in the values:
Payment = $1,500
Interest rate = 7% or 0.07
Number of periods = 10
Future Value for your investment = $1,500 x ((1 + 0.07)^10 - 1) / 0.07
Future Value for your investment = $1,500 x (1.07^10 - 1) / 0.07
Now, let's calculate the future value of your twin sister's investment. Since she contributes $1,500 annually for 30 years and earns 7 percent annually:
Payment = $1,500
Interest rate = 7% or 0.07
Number of periods = 30
Future Value for your twin sister's investment = $1,500 x ((1 + 0.07)^30 - 1) / 0.07
Now, you can use a calculator or spreadsheet to compute the values.
After calculating the future values, compare the amounts to determine who has the larger amount at age 60.