Answer:
$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
