Question

award a scholarship of $30,000 each year. The family wants the yearly awards to continue indefinitely. Assume that the fund will earn a fixed interest rate of 6% per year, compounded continuously. What is the size of the initial investment that the family must

Answer 1

size of the initial investment $500000

Step-by-step explanation:

given data

principal = $30000

rate = 6% = 0.06

solution

we get here present value that is express as here

present value =
`mP \int\limits^\alpha _0 {e^(-rt)} \, dt` .............1

put her value we get

present value =
`(1) (30000) \int\limits^\alpha _0 {e^(-0.06 t)} \, dt`

present value =
`[(e^-0.06 t)/(-0.06)]^(\alpha ) _0`

present value = $500000