Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ,
A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000

Question

​Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ​  ,  ​
A) ​$210,000 
B) ​​$200,000 
C) ​​$220,000 
D) ​​$240,000 
E) ​​$230,000

Quizplus · Accepted Answer

The formula for the present value of an annuity due is:

PV = P/i * (1 - 1/(1+i)^n)

where:
PV = present value of the annuity
P = amount paid each year
i = interest rate
n = number of years

Since the annuity is paid indefinitely, we can use the perpetuity formula:

PV = P/i

We want to solve for PV, so we have:

PV = P/i

Rearranging the formula, we get:

P = i * PV

We are given that P = $10,000 and i = 5%. Substituting these values, we get:

P = 0.05 * PV

PV = P/i = $10,000/0.05 = $200,000

Therefore, the amount of money required to set up the charitable endowment is $200,000. Answer choice B is correct.

​Determine the Amount of Money Required to Set Up a Charitable

Determine the Amount of Money Required to Set Up a Charitable