Final answer:
The future value of an annuity due calculated using simple interest for annual payments of $13,000 for three years at 3% is $41,340. A total of $39,000 was invested, and the interest earned was $2,340.
Step-by-step explanation:
To find the future value of an annuity due, we must consider that payments are made at the beginning of each period. However, the question asks to use the simple interest formula, which does not typically apply to annuities because they normally involve compound interest. Still, for the sake of following the instructions given, let's calculate the future value using simple interest.
First, let's calculate the simple interest for one annual payment of $13,000. Using the provided simple interest example:
Total future amount (with simple interest) = Principal + (Principal × interest rate × time)
For the first $13,000 payment, which will earn interest for 3 years:
Total future amount = $13,000 + ($13,000 × 0.03 × 3)
= $13,000 + $1,170 = $14,170
The second payment of $13,000 will earn interest for 2 years:
Total future amount = $13,000 + ($13,000 × 0.03 × 2)
= $13,000 + $780 = $13,780
The third payment of $13,000 will earn interest for 1 year:
Total future amount = $13,000 + ($13,000 × 0.03 × 1)
= $13,000 + $390 = $13,390
The total future value of the annuity is the sum of these amounts:
Total future value = $14,170 + $13,780 + $13,390
= $41,340
The total amount invested was the sum of the three payments, which is $13,000 × 3 = $39,000. The total interest earned is the future value minus the amount invested, which is $41,340 - $39,000 = $2,340.