Question

Find the future value of an income stream of $6000 per year, deposited into an account paying 13% interest per year, compounded continuously, over a 20-year period. Round your answer to two decimal places. Future value =$ eTextbook and Media Assistance Used Hint Assistance Used The future value of an income stream of P(t) dollars per year over an M-year period with r% interest rate (written in decimals) compounded continuously is given by

Answer 1

The future value of an income stream with continuous compounding is calculated using FV = P × ert. For $6000 per year at a 13% interest rate over 20 years, clarification is needed on how to treat multiple deposits versus a single deposit.

Step-by-step explanation:

To find the future value of an income stream of $6000 per year with a 13% interest rate compounded continuously for a 20-year period, we need to use the formula for continuously compounded interest. However, the provided formula future value = principal × (1 + interest rate)time is for discrete compounding, not continuous. For continuous compounding, the future value (FV) is calculated using the formula FV = P × ert, where P is the principal, e is the base of the natural logarithm, r is the annual interest rate in decimal form, and t is the time in years.

Since payments are made annually, we need to integrate the continuous compounding formula over the 20-year period to account for each payment made. However, without specific instructions on how to handle multiple deposits, we can either treat the scenario like a perpetuity or assume a single deposit. For a single deposit of $6000, the calculation would be:

FV = $6000 × e0.13 × 20

At this point, we need clarification on whether to consider the income stream as multiple deposits or a single deposit before proceeding.