Annuities Question! Save my Ass! (1 Viewer)

[Julz4433]

Will plans to travel to Europe and wants to deposit money in an account earning 1% per month before he goes. To ensure that he will be able to draw out $1200 per month for 7 months, starting in 1 month's time, how much should he deposit now?

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[PC]

Will plans to travel to Europe and wants to deposit money in an account earning 1% per month before he goes. To ensure that he will be able to draw out $1200 per month for 7 months, starting in 1 month's time, how much should he deposit now?!

This is a great question, because the phrase "how much should he deposit now" gives it away as a Present Value question.

Now there are two PV formulas, the big one and the little one. So which one to use? Do you know the total amount that the investment grows to (little formula), or do you know the equivalent monthly investment (big formula)? In this case, it's the monthly investment, so we use the big formula.

N is the amount we need to deposit, M = $1200, r = 1% per month = 0.01 and n = 7 months.

N = M { [(1 + r)ⁿ – 1] / r(1 + r)ⁿ }
N = 1200 { [(1 + 0.01)⁷ – 1] / 0.01(1 + 0.01)⁷ }
N = 1200 { [(1.01)⁷ – 1] / 0.01(1.01)⁷ }
N = 1200{0.07213535211/0.01072135352}
N = 1200{0.07213535211/0.01072135352}
N = $8073.83

This answer makes sense. Divide the $8073 by 7 and you'll get $1153. The rest of the $1200 each month is made up by the interest.

 

[Kat92]

This is a great question, because the phrase "how much should he deposit now" gives it away as a Present Value question.

Now there are two PV formulas, the big one and the little one. So which one to use? Do you know the total amount that the investment grows to (little formula), or do you know the equivalent monthly investment (big formula)? In this case, it's the monthly investment, so we use the big formula.

N is the amount we need to deposit, M = $1200, r = 1% per month = 0.01 and n = 7 months.

N = M { [(1 + r)ⁿ – 1] / r(1 + r)ⁿ }
N = 1200 { [(1 + 0.01)⁷ – 1] / 0.01(1 + 0.01)⁷ }
N = 1200 { [(1.01)⁷ – 1] / 0.01(1.01)⁷ }
N = 1200{0.07213535211/0.01072135352}
N = 1200{0.07213535211/0.01072135352}
N = $8073.83

This answer makes sense. Divide the $8073 by 7 and you'll get $1153. The rest of the $1200 each month is made up by the interest.

Very true, now that I look at the question for a second time. What PC said is the key to this question as it asks how much should he deposit NOW!! Which indicates that it is present value not a future value question. As in this case we don't know the future value of the annuity, we only know the amount of each contribution, M.

N=M{(1+r)^n-1/r(1+r)^n}

N = 1200 { [(1 + 0.01)^7– 1] / 0.01(1 + 0.01)^7}
N = 1200 { [(1.01)^7– 1] / 0.01(1.01)^7}
N = 1200{0.07213535211/0.01072135352}
N = 1200{0.07213535211/0.01072135352}
N = $8073.83

$8073.83/7

=$1153.

 

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