Asked by Shanna Daniels on May 27, 2024
Verified
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
Compounded Monthly
The process of adding interest to the principal sum of a loan or deposit, or compound interest, on a monthly basis.
Withdrawals
The act of taking money out of an account.
- Utilize present value equations to ascertain the amount one must invest presently to fulfill future monetary objectives.
- Familiarize yourself with the principles underlying time value of money computations.
- Deploy financial math methods to address and solve actual financial predicaments involving savings, loans, and investments.
Verified Answer
NB
nichole bennettJun 03, 2024
Final Answer :
A
Explanation :
The amount that should be deposited now can be calculated using the formula for the present value of an annuity: PV=P×[1−(1+r)−nr]PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]PV=P×[r1−(1+r)−n] , where PPP is the payment amount, rrr is the monthly interest rate, and nnn is the total number of payments. Here, P = $900 , r=4.5%12=0.00375r = \frac{4.5\%}{12} = 0.00375r=124.5%=0.00375 , and n=2×12=24n = 2 \times 12 = 24n=2×12=24 . Plugging these values into the formula gives PV=900×[1−(1+0.00375)−240.00375]PV = 900 \times \left[\frac{1 - (1 + 0.00375)^{-24}}{0.00375}\right]PV=900×[0.003751−(1+0.00375)−24] , which calculates to approximately $18,848.06.
Learning Objectives
- Utilize present value equations to ascertain the amount one must invest presently to fulfill future monetary objectives.
- Familiarize yourself with the principles underlying time value of money computations.
- Deploy financial math methods to address and solve actual financial predicaments involving savings, loans, and investments.
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