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Home Q & A Board Science-Related Homework Help Mathematics
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ikrabbe ikrabbe
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6 years ago
Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded monthly. If he puts the money in his savings account at the end of each month, what will be the present value of the balance in the account at the end of the three-year term?
A) $18 000.00
B) $18 408.04
C) $18 603.37
D) $27 284.81
E) $17 390.19
Textbook 
Contemporary Business Mathematics with Canadian Applications

Contemporary Business Mathematics with Canadian Applications


Edition: 11th
Authors:
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josanjosan
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6 years ago
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Anonymous
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#2
A year ago
Answer is $17,392.96

Annual interest rate = 2.25% compounded semiannually

Semiannual interest rate = 2.25% / 2
Semiannual interest rate = 1.125%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.01125)^2 - 1
Effective annual rate = 1.022627 - 1
Effective annual rate = 0.022627 or 2.2627%

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.022627)^(1/12) - 1
Monthly interest rate = 1.001866 - 1
Monthly interest rate = 0.001866 or 0.1866%

Monthly deposit = $500
Time period = 3 years or 36 months

Present value = $500/1.001866 + $500/1.001866^2 + … + $500/1.001866^35 + $500/1.001866^36
Present value = $500 * (1 - (1/1.001866)^36) / 0.001866
Present value = $500 * 34.785919
Present value = $17,392.96
Anonymous
wrote...
#3
10 months ago
Help! The answer is missing an explanation...
wrote...
#4
Educator
10 months ago
I am getting (C):
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