Question

You won a lottery that will make equal payments of $1,000 at the end of each year for the next five years. If the annual interest rate stays constant at 5%, what is the value of these payments in today's dollars? (Note: Round your answer to the nearest whole dollar.) $3,681 O $4,330 O $5,413 O $4,547 You found out that now you are going to receive payments of $7,500 for the next 15 years. You will receive these payments at the beginning of each year. The annual Interest rate will remain constant at 14%. What is the present value of these payments? (Note: Round your answer to the nearest whole dollar) O $46,067 O $70,097 $52,516 O $42.013

Answer 1

1. Option (b) is correct

Here, the cash inflow will be same every year, so it is an annuity. And the payments occur at the ned of each year, so it is ordinary annuity. We need to calculate the present value of annuity by the following formula:

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

where, PVA = Present value of annuity, P is the periodical amount = $1000, r is the rate of interest = 5% and n is the time period = 5

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

PVA = $1000 * (1 - (1 + 5%)^-5 / 5%)

PVA = $1000 * (1 - ( 1+ 0.05)^-5 / 0.05)

PVA = $1000 * (1 - ( 1.05)^-5 / 0.05)

PVA = $1000 * (1 - 0.78352616646) / 0.05)

PVA = $1000 * (0.21647383353 / 0.05)

PVA = $1000 * 4.329476670

PVA = $4330

So, value of these payments today is $4330.

2. Option (c) is correct

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 = $7500, r is the rate of interest = 14% and n is the time period = 15

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

PVAD = $7500 * (1 - (1 / (1 + 14%)¹⁵ / 14%) * (1 + 14%)

PVAD = $7500 * (1 - (1 / (1 + 0.14)¹⁵ / 0.14) * (1 + 0.14)

PVAD = $7500 * (1 - (1 / (1.14)¹⁵ / 0.14) * (1.14)

PVAD = $7500 * (1 - (1 / 7.13793797839) / 0.14) * (1.14)

PVAD = $7500 * ((1 - 0.14009648206) / 0.14) * (1.14)

PVAD = $7500 * (0.85990351793 / 0.14) * (1.14)

PVAD = $7500 * 6.14216798522 * 1.14

PVAD = $52516

So, value of these payments today is $52516.