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Consider a series of end-of-period CFs spanning 2040-2050, which increase by a fixed amount each period. The amount of the first CF in the series is $149 and the increment is $76. The nominal interest rate is 1.3%; compounding occurs 5 times per year. What is the equivalent value of this series at the beginning of 2040

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Answer:

The equivalent value of the series=$ 10,536.61

Explanation:

An annuity is a series of equal payment or receipt occurring for certain number of period.  

The series of cash flows of $149 and the increase $76 occurring for 10 years are example of ordinary annuity.

So we can workout their present value using the formula stated below:

This is done as follows:

The Present Value of annuity = A × (1- (1+r)^(-n))/r

Present value of  series of fixed amount  cashflow

A- periodic cash flow-149, r- semi annual rate of interest - 1.3/5= 0.26%  

n- number of period- (10×5) = 50.

Present value = 149× (1-1.0026^(-50)/0.0026=6,977.57

Present value of the increment series of cashflow

A- periodic cash flow-76, r- semi annual rate of interest - 1.3/5= 0.26%  

n- number of period- (10×5) = 50.

Present value = 76× (1-1.0026^(-50)/0.0026=3,559.03

The equivalent value of the series = Present value of the fixed amount + present value of the increment= 6,977.57 + 3,559.03= 10536.61

The equivalent value of the series=$ 10,536.61

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