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Question 1180022: Is it C? I want to check my answer.
Topic: Financial Mathematics
Jackson wants to have $18,000 available to buy a motorcycle in three years. How much should Jackson save each month if he earns 5% interest, compounded monthly?
The question is provided in the link here: https://i.imgur.com/HkeaBdW.png
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849)   (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
The answer is actually choice A, in the upper-left corner. In other words, in the north-west corner.
He must save $464.48 per month.
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Further explanation:
We use the future value of annuity formula. Specifically the "ordinary" version, and not the "annuity due" version. This is because Jackson deposits at the end of the month, rather at the first of it.
Jackson wants to have FV = 18,000 in his account after n = 3*12 = 36 months.
The decimal form of the interest rate per month is i = r/12 = 0.05/12 = 0.004167 approximately; though often times its better to stick with the fraction form as the answer choices indicate.
The future value of ordinary annuity is
FV = P*( (1+i)^n - 1)/i
where P is the monthly payment or deposit
Solving for the monthly payment/deposit P gets us the following:
FV = P*( (1+i)^n - 1)/i
FV*i = P*( (1+i)^n - 1)
P*( (1+i)^n - 1) = FV*i
P = FV*i/( (1+i)^n - 1)
Basically the original fraction term ( (1+i)^n - 1)/i flipped to i/( (1+i)^n - 1), and we change which of the P and FV were isolated.
So that explains why each answer choice has the format of dividing FV*i over top ( (1+i)^n - 1)
Again, i = 0.05/12 and n = 12*3
So far, we narrowed the answer between the two left-side panels. Both upper expressions for these panels are identical. The only difference is the calculated result shown underneath. Use your calculator to compute the expression. It might help to do it in two pieces.
Up top we have: 18000*0.05/12 = 75
Down below we have: (1+0.05/12)^36-1 = 0.16147223 approximately
Divide the two results: 75/0.16147223 = 464.47615172
That rounds to 464.48
He needs to deposit $464.48 per month, for 36 months, so that at the end of the three year period he'll have $18,000
So that's why the answer is the upper-left corner.
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