Question

A business is planning to purchase a piece of equipment that will produce a continuous stream of income for 5 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.)

1) What is the future value of the investment?

2) What is the present value of the investment?

Answer 1

No. of years = 5

Continuous payments = 7000

Interest rate (r ) = 6.65% or 0.065

(a) Future value of annual payments = P * { (1+r)^n - 1 } / r

7000*(((1+0.065)^5)-1)/0.065

39855.48683

So, Future value of investment is $39,855.48

(b) Present value of annual payments = Annual amount * [ 1 - {1/((1+r)^n) ] / r

Present value of investment = 7000 * (1 - (1/ (1 +0.065)^5))/ 0.065

Present Value of investment = $29,089.76

So, Present Value of investment is $29089.76.

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