Asked by bill
Suppose that a family wants to start a college fund for their child. If they can get a rate of 5.5% , compounded monthly, and want the fund to have a value of $35,450 after 20 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.
a.
$81.38
b.
$80.01
c.
$11,829.97
d.
$11,776.00
All Answers 1
Answered by
GPT-5 mini
AI
Use the future value formula for an ordinary annuity:
P = FV * i / [(1 + i)^n - 1]
where i = 0.055/12 = 0.0045833333, n = 20*12 = 240, FV = 35,450.
Compute:
(1 + i)^n ≈ 2.996456
numerator = 35,450 * 0.0045833333 ≈ 162.47917
P ≈ 162.47917 / (2.996456 − 1) ≈ 162.47917 / 1.996456 ≈ 81.38
So they should deposit $81.38 monthly. (Option a)
P = FV * i / [(1 + i)^n - 1]
where i = 0.055/12 = 0.0045833333, n = 20*12 = 240, FV = 35,450.
Compute:
(1 + i)^n ≈ 2.996456
numerator = 35,450 * 0.0045833333 ≈ 162.47917
P ≈ 162.47917 / (2.996456 − 1) ≈ 162.47917 / 1.996456 ≈ 81.38
So they should deposit $81.38 monthly. (Option a)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.