Financial Management 2

3 Example A. **Could you create the new one for me, as below I find the Internet that it is plagiarism**

A. You have just won the Strayer Lottery jackpot of $11,000,000. You will be paid in 26 equal annual installments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding of interest. What is the present value of the payments you will receive?

1. Strayer Lottery Jackpot

Jackpot $11,000,000

Annual Installments 26

Interest Rate 9%

PV ?

Monthly

Compounded

Installments 312

Interest Rate 0.75%

PV of payment $1,068,896.32

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2. Quoted Annual Interest Rate = 9%

Compounded Period = 12 periods in a year

Monthly Compounded interest rate = 0.075 (9%/12)

Calculate Effective Percentage Rate (EFF)

EFF =(1+0.0075) ^ 12 - 1.0

(1.0075)^12 -1.0

1.093807 - 1.0

0.093807

9.3807%

Future Value No. of periods

$11,000,000/26 periods = $423,076.92

Calculate Present Value

PV = (rate,nper,pmt,fv,type)

Rate = 0.093807

No. periods = 26

Pmt = 423,076.92

Future Value = 0

Type = 1

PV = (0.09387, 26, 423,076.92, 0, 1)

PV = $4,453,789.94

The present value of the payments you will receive is $4,453,789.94.

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3. The formula for the present value of an anuallity is:

PV = A * [ 1 - (1 + r) ^ (-n) ] / r

Here:

A = 11000000 / 26 = 423076.92

r is the effective rate of 9% monthly compounded

r = (1 + 0.09/12) ^ (12) - 1 = 1.0938 - 1 = 0.0938

n = 26

Then, PV =  423,076.92 * [1 - (1+0.0938)^(-26) ] / (0.0938)

PV = 4,072,055.25

(Comment Exam 3 is “This was closer than what I came up with. The answer when we went over it in class was $4,453.789.94. Only 1 person we were told got it right.”)