Question

LaQuesha Jackson has made a considerable fortune. She wishes to start a perpetual scholarship for engi- neering students at her school. The scholarship will provide a student with an annual stipend of $10,000 for each of 4 years (freshman through senior), plus an additional $5000 during the senior year to cover job search expenses. Assume that students graduate in 4 years, and the money is paid at the beginning of each year with the first award at the beginning of Year 1. The interest rate is 10%.
Required:
a. Determine the equivalent uniform annual cos (EUAC) of providing the scholarship.
b. How much money must LaQuesha donate?

Answer 1

Answer:

A)  EUAC = 38625.09 / 3.4869 = 11077.354

B) $83225.79

Explanation:

A ) Determining the EUAC  of providing the scholarship

EUAC = sum of present values / sum of present value factors

present value is calculated as ( p ) =  year * present value factor

the present value factor for the various(4) years are : ( 1.000, 0.9091,0.8264,0.7513 ) = 3.4869

present value for the 4 years =( $10000 , $9,090.91, 8264.46, 11269.72 )

total = $38625.09

therefore EUAC = 38625.09 / 3.4869 = 11077.354

B ) THE MONEY LAQUESHA MUST DONATE

interest rate for perpetuity = 1.10 ^4 - 1

                                             = 1.4641 -1 =  0.4641

therefore amount to be donated = total present value / interest rate for perpetuity    

= 38625.09 / 0.4641  = $83225.79