Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year

$31,874

Explanation:

In this question, we are asked to calculate how much Dan would have at the end of the 10th year if he contributes a maximum of $2000 at the end of each year for the next 10 years and earns 10% on his contribution.

This kind of problem can be solved using the annuity formula I.e the annuity formula can be used to calculate the accumulated value at the end of the 10th year.

Annuity refers to a series of payment that is made at equal time intervals

Mathematically, the future value of an annuity =

Annuity payment * [(1 + r)^n - 1]/r

Where r is the discount rate and n is the number of years.

In this question, we have identified the following to be used in the formula.

Annuity payment = the maximum payable contribution per year = $2000

Number of years = 10 years

The discount rate = 10% = 10/100 = 0.1

We plug these values in the formula:

Future accumulated value = 2,000 * [(1+0.1)^10 - 1]/0.1 = 2,000 * [(1+0.1)^10 - 1)]/0.1

= 2,000 * (2.5937-1)/0.1 = 2,000 * (1.5937)/0.1 = 2,000 * 15.937 = $31,874

The accumulated value of the annuity payment is $31,874

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