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

Answer:

size of the initial investment $500000

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 =    $[\frac{e^-0.06 t}{-0.06}]^{\alpha } _0$  

present value = $500000