An endowment of $25,000,000 is to be split among 3 elite Universities. This money will be amortised over a period of 25 years @ 8% compounded annually and indexed for inflation @ 3% per year. University A will receive a certain amount at the end of the 1st.year. University B will receive 1.5 times University A. University C will receive 2 times University B. These monies will be strictly allocated for awarding annual scolarships. What are the initial payments that each University will receive? Thanks for any help.
There are a number of ways of solving this problem. I will use the simplest of them as follows:
First, will find the net interest rate by: 1.08 / 1.03 =4.85%. Using this rate, will find the PV of the rarios
of disbursements, which are as follows: 1 + 1.5 + 3 =5.5, using the common TVM formula:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=5.5{[1+0.0485]^25 - 1.[1+0.0485]^-25}. 0.0485^-1=78.66089675
Now, we simply divide $25 million by this last number=$25,000,000 / 78.66089675=$317,819.92. This is the 1st. payment to University A. The only adjustment we have to make is to index it to inflation rate:
$317,819.92 x 1.03 =$327,354.52. So, we have:
1) $327,354.52- First annual payment to University A.
2) $327,354.52 x 1.5 =$491,031.78-First payment to University B.
3) $491,031.78 x 2 =$982,063.56-First payment to University C.
4)$1,800,449.86-Is the total first year payments to all 3 Universities. These individual payments will be indexed by 3% inflation rate every year thereafter for 25 years.
Also, all the three combined payments for the first year can be directly calculated using a familiar TVM formula, which we can plug into Wolfram/Alpha, and which gives an instantaneous result:
http://www.wolframalpha.com/input/?i=1,213,592.233*((1+%2B+0.04854368932)%5E25+%2F+((1+%2B0.04854368932)%5E25+-+1))+*+1.03
