Question

You plan to save $200 every month for the next 30 years for retirement. You invest in an annuity paying 3% compounded monthly. How much will be in the annuity 30 years from now? Enter a number rounded to two decimal places with no dollar sign or commas.

Answer 1

To calculate the amount in the annuity after 30 years, we can use the formula for the future value of an annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Monthly deposit amount ($200)

r = Monthly interest rate (3% = 0.03)

n = Number of compounding periods (30 years * 12 months/year = 360 months)

Let's substitute the values into the formula:

FV = 200 * [(1 + 0.03)^360 - 1] / 0.03

Calculating the value inside the brackets first:

(1 + 0.03)^360 ≈ 4.0397

Now, substitute the value into the formula:

FV ≈ 200 * (4.0397 - 1) / 0.03

Simplifying the equation:

FV ≈ 200 * 3.0397 / 0.03

FV ≈ 20,198

Therefore, the amount in the annuity 30 years from now will be approximately $20,198.