Question

An ordinary annuity selling at $4,947.11 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity’s appropriate interest rate (IN) remains at 6.50% during this time, the annual annuity payment (PMT) will be ________. You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in eight equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won ________ assuming annual interest rate of 6.50%.

Answer 1

Answer:

$812.49 and $28,369,687.5

Explanation:

Let us assume the annual payments be X

Sale of ordinary annuity = X × PVAF factor

$4,947.11 = X  × PVAF(6.5%, 8 years)

$4,947.11 = 6.0888 × X

X = $812.49

And,

The Present value is

Present value = Annual payments + Annual payments × PVAF factor

= $4,375,000 + $4,375,000 × PVAF(6.5%, 7 years)

= $4,375,000 + $4,375,000 × 5.4845

= $28,369,687.5

The $4,375,000 is come from

= $35,000,000 ÷ 8 years

= $4,375,000

Refer to the PVAF factor table

We simply applied the above formulas