Mary Alice just won the lottery and is trying to decide between the options of receiving the annual cash flow payment option of $270,000 per year for 20 years beginning today, or receiving one lump-sum amount today. Mary Alice can earn 4% investing this money. At what lump-sum payment amount would she be indifferent between the two alternatives?

The lump sum payment is $3,669,389

Explanation:

Solution

Recall that:

The annual cash flow payment option is =$270,000

n = 20 years

Mary Alice can earn =4% investment of the money

Now

We find the lump sum payment which is given below:

Lump-sum amount = $270,000* PVAF at (4%,20y)

Thus

$270,000*13.590326344968

= $3,669,389

Note: It would be of no difference between two alternatives when lump-sum amount is produced by bringing the alternative 1 cash flows $270,000 in the present value by using the PVAFat 4%,20

PVAF =Present value annuity factor

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"we first find value of tax in dollars.

the difference between the two prices   is: 23. 54 - 22 = 1.54

therefore the sales tax in dollars is 1.54

the tax % will be   (amount of tax / original cost price ) × 100

(1.54 / 22) × 100  → (0.07) × 100 =   7

so the tax rate is 7%

we can double check the answer.

7 % of 22   → (7/100) × 22 → 0.07 × 22 = 1.54

22 + 1.54 = 23.54"