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he local botanical society wants to ensure that the gardens in the town park are properly cared for. The group recently spent $100,000 to plant the gardens. The members want to set up a perpetual fund to provide $100,000 for future replantings every 10 years. a) If interest is 5%, how much money is needed for the fund?b) If the last replanting is in year 100, how much

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Answer:

Instructions are listed below.

Explanation:

Giving the following information:

The members want to set up a perpetual fund to provide $100,000 for future replantings every 10 years. The interest rate is 5%.

I will assume that the money is deposited as a lump sum:

FV= PV* (1 + i)^n

PV= FV/ (1+i)^10

PV= 100,000 / 1.05^10= $61,391.33

Now, if n is 100 years:

PV= 100,000/ 1.05^100= $760.45

a. The money that are required in the future is  $159010.

b. The amount should be $157801.

Calculation of the amount:

a.

Since R = 5%

Periodic cost for each 10 years required = $100000

Time = infinite or perpetuity

So,

Value of perpetual fund, today = 100000*(A/F, 5%, 10)/5%

= 100000*.079505/5%

= $159010

B.

When Time = 100 years

R = 5%

And, Periodic cost for each 10 years required = $100000

So,

PW of the funds required = 100000*(A/F, 5%, 10)*(P/A, 5%, 100)

= 100000*.079505*19.847910

= $157800.81 or $157801

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