The accumulated value of n payments of $500 at i immediately after the n^th payment is S.Which of the following gives the correct accumulated value immediately after the (n+2)^th payment of $500? A)S(1 + i)+ 2(500)(1 + i) B)S + 500(1 + i)+ 500 C)[S + 500](1 + i)² + 500 D)S(1 + i)² + 500(1 + i)+ 500

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Quizplus · Accepted Answer

The accumulated value of n payments of $500 at i immediately after the n^th payment is given as: A = $500 * [(1+i)^n - 1]/i We need to find the accumulated value immediately after the (n+2)^th payment of $500. This means we have made (n+2) - (n+1) = 1 payment, and the accumulated value will be: A' = A(1+i) + $500(1+i) Substituting the expression for A, we get: A' = [$500 * [(1+i)^n - 1]/i](1+i) + $500(1+i) Simplifying this expression, we get: A' = S(1+i)² + $500(1+i) + $500 This matches the expression given in option D, and hence D is the correct answer.

The Accumulated Value of N Payments of $500 at I