Question

You need $40,000 in ten years for the purchase of a new car for your nephew...

You need $40,000 in ten years for the purchase of a new car for your nephew who will be graduating college.  You currently have $20,000 saved and want to invest it for ten years at a 6% rate of return.

  1. Will you be able to achieve your investment goal in ten years?

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  1. If not, then how much more would you need to invest today, instead of the $20,000, to accumulate that goal in ten years?

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  1. If not, and you do not have the extra money to invest now then how much of a return (interest rate) would you need to earn in order to achieve your goal?

Answer

  1. If this rate of return involves too much risk, and if you cannot invest more at this time, then how much would you need to invest each year to accumulate your investment goal in ten years?

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  1. If you determine that none of the above options are viable then how long would it take to accumulate the full investment goal if you invest $20,000 now at your rate assumption (see below) with no annual additions?

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Answer #1

You need $40,000 in ten years for the purchase of a new car for your nephew who will be graduating college. You currently have $20,000 saved and want to invest it for ten years at a 6% rate of return.

Will you be able to achieve your investment goal in ten years?

FV = PV * (1+r %) ^n

Where,

Future value of investment FV =?

Present value of investment PV = $20,000

Interest rate r = 6% per year

Time period n = 10 years

Therefore

FV = $20,000 * (1 + 6%) ^10

FV = $35,816.95

Therefore the future value (FV) of your investment will be $35,816.95 and you will not be able to achieve your target

If not, then how much more would you need to invest today, instead of the $20,000, to accumulate that goal in ten years?

FV = PV * (1+r %) ^n

Where,

Future value of investment FV =$40,000

Present value of investment PV =?

Interest rate r = 6% per year

Time period n = 10 years

Therefore

$40,000 = PV * (1 + 6%) ^10

PV = $40,000/ (1 + 6%) ^10

=$22,335.79

Therefore you need to investment $22,335.79

If not, and you do not have the extra money to invest now then how much of a return (interest rate) would you need to earn in order to achieve your goal?

FV = PV * (1+r %) ^n

Where,

Future value of investment FV =$40,000

Present value of investment PV =$20,000

Interest rate r=?

Time period n = 10 years

Therefore

$40,000 = $20,000 * (1 + r) ^10

$40,000/ $20,000 = (1 + r) ^10

Or 2 = (1 + r) ^10

Or r = 7.18%

If this rate of return involves too much risk, and if you cannot invest more at this time, then how much would you need to invest each year to accumulate your investment goal in ten years?

In part 1 you have future value after 10 years = $35,816.95

But you need future value of $40,000 after 10 years

Therefore remaining amount = $40,000 -$35,816.95 =$4,183.05

Now calculate the money required to invest each year to accumulate your investment goal in ten years in following manner –

Now we can use FV of an Annuity formula to calculate the annual deposits by you

FV = PMT *{(1+r) ^n−1} / r

Where,

Future value of annual deposits FV =$4,183.05

PMT = Annual deposits =?

n = N = number of payments = 10 years

r = I/Y = interest rate per year = 6%

Therefore,

$4,183.05 = Annual deposit *{(1+ 6%) ^10−1} /6%

Annual deposits = $317.36

Therefore you have to deposit $317.36 per year to achieve your goal.

If you determine that none of the above options are viable then how long would it take to accumulate the full investment goal if you invest $20,000 now at your rate assumption (see below) with no annual additions?

FV = PV * (1+r %) ^n

Where,

Future value of investment FV =$40,000

Present value of investment PV =$20,000

Interest rate r = 6% per year

Time period n =?

Therefore

$40,000 = $20,000 * (1 + 6%) ^n

$40,000/$20,000 = (1 + 6%) ^n

Or 2 = (1 + 6%) ^n

Or n = 11.90 years

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