If the interest rate is 5% and will be 5% forever, the present value of an income stream consisting of $10 a year paid to you on February 11 of every year, starting right now, is $210.

Question

Quizplus · Accepted Answer

The present value of an income stream can be calculated using the formula: PV = CF/(1+r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods.

In this case, the cash flow is $10/year, the interest rate is 5%, and the payments are made annually starting immediately. Therefore, the present value can be calculated as follows:

PV = $10/(1+0.05)^0 + $10/(1+0.05)^1 + $10/(1+0.05)^2 + ... + $10/(1+0.05)^n

Since the payments are made forever, we can use the formula for the present value of a perpetuity, which is PV = CF/r. Therefore, the present value is:

PV = $10/0.05 = $200

However, the question asks for the present value on February 11 of every year, which means we need to discount the cash flows to that date. If we assume a 365-day year, then there are 365/365 = 1 period between February 11 of this year and February 11 of next year. Therefore, the present value on February 11 of this year is:

PV = $10/(1+0.05)^0 = $10

And the present value on February 11 of next year is:

PV = $10/(1+0.05)^1 = $9.52

The total present value of the income stream is the sum of these two values:

PV = $10 + $9.52 = $19.52

This is not equal to $210, so the statement is false.

If the Interest Rate Is 5% and Will Be 5