Question

The 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 is needed for the fund?

Answer 1

To set up a perpetual fund to provide $100,000 for future replantings every 10 years, the local botanical society needs $102,857.50, assuming an interest rate of 5%. If the last replanting is in year 100, the same amount of $102,857.50 is needed for the fund.

Step-by-step explanation:

a) To calculate the amount needed for the fund, we can use the formula for the present value of an annuity:

PV = PMT * ((1-(1+r)^(-n))/r)

Where PV is the present value, PMT is the future value per period, r is the interest rate, and n is the number of periods. In this case, the future value per period is $100,000, the interest rate is 5%, and the number of periods is 10. Plugging these values into the formula, we get:

PV = $100,000 * ((1-(1+0.05)^(-10))/0.05) = $102,857.50

So, $102,857.50 is needed for the fund.

b) To calculate the amount needed for the fund if the last replanting is in year 100, we need to first find the number of periods. In this case, the number of periods is 100 / 10 = 10. Plugging this value into the formula, along with the future value per period of $100,000 and the interest rate of 5%, we get:

PV = $100,000 * ((1-(1+0.05)^(-10))/0.05) = $102,857.50

So, $102,857.50 is needed for the fund