Question

you just won the $89 million california state lottery. the lottery offers you a choice of receiving a lump sum today or $89 million split into 26 equal annual installments at the end of each year (with the first amount paid a year from now). assume the funds can be invested at an annual rate of 7.65%. what dollar amount of the lump sum would exactly equal to the present value of the annual installments? round off to the nearest $1: group of answer choices $13,092,576 $89,000,000 $41,083,128 $38,163,612

Answer 1

$38,163,612 is the amount of the lump sum calculated that would be equivalent to the annual installments' present value (PV).

Step-by-step explanation:

The present value of the annual installments can be calculated using the formula for the present value of the annuity. The formula is:

`\[ PV = PMT * \left((1 - (1 + r)^(-n))/(r)\right) \]`

Where PV denotes the present value, PMT denotes the annual payment, r denotes the interest rate, and n denotes the number of years. In this case, the annual payment is $89 million, the interest rate is 7.65%, and the number of years is 26. When we insert these figures we arrive at:

`\[ PV = 89,000,000 * \left((1 - (1 + 0.0765)^(-26))/(0.0765)\right) \]`

Calculating this equation gives us a present value of approximately $38,163,612. Therefore, the dollar amount of the lump sum that would equal the present value of the annual installments is $38,163,612.

Answer 2

The dollar amount of the lump sum that would be equal to the present value of the annual installments is $530,963,362.

Step-by-step explanation:

To determine the dollar amount of the lump sum that would be equal to the present value of the annual installments, we need to calculate the present value of the annuity. We can use the formula:

PV = C imes (1 - (1 + r)^{-n}) / r

Where PV is the present value, C is the annual payment, r is the interest rate, and n is the number of periods. In this case, the annual payment is $89 million, the interest rate is 7.65%, and the number of periods is 26. Plugging in these values, we get:

PV = 89,000,000 imes (1 - (1 + 0.0765)^{-26}) / 0.0765

Solving this equation, we find that the present value of the annuity is approximately $530,963,362. Therefore, the dollar amount of the lump sum that would be equal to the present value of the annual installments is $530,963,362.