28.07.2022 - 00:13

# (a) Find the present and future value of an income stream of $6000 per year for a period of 10 years if the interest rate compounded continuously, is 2%. Round your answers to two decimal places. Present value =$ boxed{space} Future value = $boxed Question: (a) Find the present and future value of an income stream of {eq}\displaystyle$6000 {/eq} per year for a period of {eq}\displaystyle 10 {/eq} years if the interest rate compounded continuously, is {eq}\displaystyle 2%. {/eq}

Present value {eq}\displaystyle = $boxed{space} {/eq} Future value {eq}\displaystyle =$ boxed{space} {/eq}

(b) How much of the future value is from the income stream? How much is from interest?

The amount from the income stream is {eq}\displaystyle $boxed{space}. {/eq} The amount from the interest is {eq}\displaystyle$ boxed{space}. {/eq}
• (a) To find the present value of the income stream, we can use the formula: PV = A / r (1 - 1/ e^(rt)) where PV is present value, A is the annual income, r is the interest rate, t is the number of years, and e is the mathematical constant 2.71828. Plugging in the given values, we get: PV = 6000 / 0.02 (1 - 1/ e^(0.02*10)) PV = $50,124.41 To find the future value, we can use the formula: FV = PV * e^(rt) Plugging in the given values, we get: FV = 50,124.41 * e^(0.02*10) FV =$67,080.22 Therefore, the present value is $50,124.41 and the future value is$67,080.22. (b) To find out how much of the future value is from the income stream and how much is from interest, we can subtract the present value from the future value to get the total interest earned. Then we can subtract the total interest from the future value to get the amount from the income stream. Total interest earned = FV - PV Total interest earned = 67,080.22 - 50,124.41 Total interest earned = $16,955.81 Amount from income stream = FV - total interest earned Amount from income stream = 67,080.22 - 16,955.81 Amount from income stream =$50,124.41 Amount from interest = Total interest earned Amount from interest = $16,955.81 Therefore, the amount from the income stream is$50,124.41 and the amount from interest is $16,955.81. Do you know the answer? Not sure about the answer? Find the right answer to the question (a) Find the present and future value of an income stream of$6000 per year for a period of 10 years if the interest rate compounded continuously, is 2%. Round your answers to two decimal places. Present value = $boxed{space} Future value =$ boxed by subject Business, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.