Winnie Winalot has won the Set for Life lottery and will receive a payment of $77,326.76...

Winnie Winalot has won the Set for Life lottery and will receive a payment of $77,326.76 every year, starting today, for the next 20 years. If Winnie invests the proceeds at a rate of 7.84 percent per annum, what will be the present value of the cash flows she will receive?

Expert Solution

Here, the cash inflows will be same every year, so it is an annuity. And since the cash flows will start at the beginning of each year so it will be termed as an annuity due. For calculating the present value of annuity due, we will use the following formula:

PVAD = P * (1 - (1 / (1 + r)n / r) * (1 + r)

where, PVD is the present value of annuity due, P is the periodical amount = $77326.76, r is the rate of interest = 7.84% and n is the time period = 20

Now, putting these values in the above formula, we get,

PVAD = $77326.76 * (1 - (1 / (1 + 7.84%)20 / 7.84%) * (1 + 7.84%)

PVAD = $77326.76 * (1 - (1 / (1 + 0.0784)20 / 0.0784) * (1 + 0.0784)

PVAD = $77326.76 * (1 - (1 / (1.0784)20 / 0.0784) * (1.0784)

PVAD = $77326.76 * (1 - (1 / 4.5247812051) / 0.0784) * (1.0784)

PVAD = $77326.76 * ((1 - 0.22100516128) / 0.0784) * (1.0784)

PVAD = $77326.76 * (0.77899483871 / 0.0784) * (1.0784)

PVAD = $77326.76 * 9.93615865711 * 1.0784

PVAD = $828568.10

So, required present value is $828568.10

jeff jeffy answered 1 year ago

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