The grand prize in an Illinois lottery is 5000000 which will

The grand prize in an Illinois lottery is $5000000, which will be paid out in 25 equal annual payments of $200000 each. Assume the first payment of $200000 is made, leaving the state with the obligation to pay out $4800000 in 24 equal yearly payments of $200000 each. How much does the state need to deposit in an account paying 10% compounded annually to achieve this? Round your answer to 2 decimal places. $

Solution

total amount to be paid; $200,000 for 24 months;

10% per month;

Total amount to be paid 200,000*24 = $4,800,000;

EMI = P*r*(1+r)^n/((1+r)^n-1);

200,000 = P*(0.1/12)((1+0.1/12)^24)/((1+0.1/12)^24-1);

P = ((1+0.1/12)^24-1)*200,000 / (((1+0.1/12)^24)*(0.1/12));

P = $4334171;

Is the amount;