A business is planning to purchase a piece of equipment that will produce a cont

Question

A business is planning to purchase a piece of equipment that will produce a continuous stream of income for 8 years with rate of flow f(t) = 7,000. If the continuous income stream earns 6.65%, compounded continuously, what single deposit into an account earning the same interest rate will produce the same future value as the continuous income stream (This deposit is called the present value of the continuous income stream.) What is the future value of the investment? (Round to the nearest dollar as needed.)

Explanation / Answer

answer to question 1 -

per year income = 7000 for 8 years

earning interest rate = 6.65% compounded continously

so the value in your account after 7 months if you deposit earned income as follows -

now computation of single amt. which would be deposit now and equivalent to this value

71497.26 = principal*(1+0.0665/365)^(365*8)

principal amt. = 71497.26/1.702251

= 42001.59
future value of investment = 71497.26

answer to question no.2 -

as furniture store earns more by 1000 so obvious future value of the same after 7 years has greater than computer store.

now future value of furniture store are as follows -

now future value of computer store is as follows -

now compare both of them. you will find that the furniture store has higher future value.

Please comment in case of further clarification required.

year installment Holding period Amt. 1 7000 7 11149.20 2 7000 6 10431.96 3 7000 5 9760.85 4 7000 4 9132.92 5 7000 3 8545.39 6 7000 2 7995.65 7 7000 1 7481.28 8 7000 0 7000.00 71497.26

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