Question

your grandmother is sending you money. She is giving you two options. Receive $1000 today or 1150 after 4 years. At what required rate would you be interested in the option of receiving 1150 after 4 years.

Answer 1

To be indifferent between receiving $1000 now and $1150 in 4 years, the required annual interest rate would be approximately 3.57%, calculated using the future value formula.

Step-by-step explanation:

The student is asking a financial mathematics question, specifically about the time value of money and compound interest. The real-world application in this context involves determining the rate of return or interest one would need to prefer receiving $1150 after 4 years instead of $1000 today. As such, we will use the formula for the future value of a single sum, which is Future Value (FV) = Present Value (PV) * (1 + Interest Rate)^{number of periods}. Plugging in the given values we get:

1150 = 1000 * (1 + r)^4

Where r represents the required rate of interest. Solving for r, we divide both sides by 1000, and then take the fourth root:

(1150 / 1000) = (1 + r)^4

((1150 / 1000)^(1/4)) - 1 = r

Using a calculator, this comes out to approximately:

r = 0.0357 or 3.57%

Thus, you would need an interest rate of at least 3.57% to be indifferent between receiving $1000 now or $1150 in four years.

Answer 2

To determine the required rate at which you would be interested in receiving $1150 after 4 years instead of $1000 today, we need to calculate the future value of $1000 after 4 years using compound interest.

Step-by-step explanation:

To determine the required rate at which you would be interested in receiving $1150 after 4 years instead of $1000 today, we need to calculate the future value of $1000 after 4 years using compound interest. Let's assume a compounded annual rate of return, r, and the formula for compound interest:

Future Value (FV) = Present Value (PV) * (1 + r)^n

Given that PV = $1000, FV = $1150, and n = 4, we can rearrange the formula to solve for r:

r = (FV/PV)^(1/n) - 1

Plugging in the values, we have:

r = ($1150/$1000)^(1/4) - 1

Solving this equation will give us the required rate at which you would be interested in receiving $1150 after 4 years.