If payment into the annuity is done at the beginning of the period, and the value is measured at the end of the period, the total value is

$23,000(1+10%)(1+10%)(1+10%) +

$23,000(1+10%)(1+10%) +

$23,000(1+10%) = $23,000(1+10%)(1 + (1+10%) + (1+10%)(1+10%))

= $23,000(1.10)(2.10 + 1.21) = $23,000(1.1)(3.31) = $83,743

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The amount 23k*1.1

$23,000(1+10%)(1+10%)(1+10%) +

$23,000(1+10%)(1+10%) +

$23,000(1+10%) = $23,000(1+10%)(1 + (1+10%) + (1+10%)(1+10%))

= $23,000(1.10)(2.10 + 1.21) = $23,000(1.1)(3.31) = $83,743

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The amount 23k*1.1

^{3}represents the value of the first payment after 3 years; the amount 23k*1.1^{2}represents the value of the second payment after it has been earning interest for 2 years; 23k*1.1 is the value of the final payment after it has earned interest for 1 year. If you have a longer string of payments, there is a formula for figuring this, but it is more complicated than necessary for this problem.