Anita is planning to go back to school in 2 years. Once at school, she wishes to be able to withdraw $900 at the end of each month for 2 years. If interest is 4.5% compounded monthly, determine the amount that should be deposited now to fulfil her goal.

A) $18,848.06
B) $19,675.25
C) $20,437.43
D) $20,884.13
E) $21,973.28

Question

nichole bennett · Accepted Answer

Final Answer : A, Explanation :   The amount that should be deposited now can be calculated using the formula for the present value of an annuity:   P V = P × [ 1 − ( 1 + r ) − n r ] PV = P 	imes \left[\frac{1 - (1 + r)^{-n}}{r}ight] P V = P × [ r 1 − ( 1 + r ) − n ​ ]  , where   P P P   is the payment amount,   r r r   is the monthly interest rate, and   n n n   is the total number of payments. Here,   P = $900  ,   r = 4.5 % 12 = 0.00375 r = \frac{4.5\%}{12} = 0.00375 r = 12 4.5% ​ = 0.00375  , and   n = 2 × 12 = 24 n = 2 	imes 12 = 24 n = 2 × 12 = 24  . Plugging these values into the formula gives   P V = 900 × [ 1 − ( 1 + 0.00375 ) − 24 0.00375 ] PV = 900 	imes \left[\frac{1 - (1 + 0.00375)^{-24}}{0.00375}ight] P V = 900 × [ 0.00375 1 − ( 1 + 0.00375 ) − 24 ​ ]  , which calculates to approximately $18,848.06.

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