Question

Find the future value of the given discrete income stream. Weekly payments of $150; i = 2.1%; t=8 years, compounded continuously. The future value of the income stream will be $___?

Answer 1

To find the future value of the given income stream, we can use the formula for continuous compound interest: Future Value = Present Value * e^(interest rate * time). In this case, the future value of the income stream, compounded continuously, is approximately $179.44.

Step-by-step explanation:

To find the future value of the given income stream, we can use the formula for continuous compound interest:

Future Value = Present Value * e^(interest rate * time)

In this case, the present value is $150, the interest rate is 2.1% (or 0.021 as a decimal), and the time is 8 years.

Plugging in the values, we get:

Future Value = $150 * e^(0.021 * 8)

To calculate the future value, you can use a scientific calculator or an online calculator that has an exponential function. The future value of the income stream, compounded continuously, is approximately $179.44.

Answer 2

In this case, the future value of the income stream will be approximately $186.91.

Step-by-step explanation:

To find the future value of the given discrete income stream, we can use the formula for continuous compound interest:

`FV = P*e^(r*t)`

Where FV is the future value, P is the initial payment, r is the interest rate, and t is the time period.

In this case, the initial payment (P) is $150, the interest rate (r) is 2.1% (expressed as a decimal), and the time period (t) is 8 years. Plugging in these values into the formula, we get:

`FV = 150*e^(0.021*8)`

Solving this equation, the future value of the income stream will be approximately $186.91.