# supposed S= 9 + 9/1.07 + 9/1.07^2 + ...+ 9/1.07^961, Find Value of S. (please break down in step by step)

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supposed S= 9 + 9/1.07 + 9/1.07^2 + ...+ 9/1.07^961, Find Value of S. (please break down in step by step)

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Step 1

This is a problem of finding the present value of \$ 9 received for 962 periods (i.e. 1+961) periods at a interest rate of 7%.

The first payment has been received at Period -0 and therefore, the present value is same as that of amount received i.e. \$ 9.

Step 2

The second payment has been received at the end of Period-1. Therefore, it has been discounted at the rate of 7% for one time. (i.e. divided the amount received by (1+rate) i.e (1+0.07)

The third payment has been received at the end of Period-2. Therefore, it has been discounted at the rate of 7% for twice. (i.e. divided the amount received by (1+rate) twice i.e. (1+0.07)^2)

The fourth payment has been received at the end of Period-3. Therefore, it has been discounted at the rate of 7% thrice (divided the amount received thrice by (1+rate) i.e. (1+0.07)^3)

The process continues till the final payment received at the end of Period -961. Therefore it has been discounted at the rate of 7% 961 times (i.e. divided the amount received 961 times i.e. (1+0.07)^961)

Step 3

The mathematical computation has been shown for first 10 payments received i.e. upto the end of period-9, as under:

The Mathematical formula to compute the discount factor i.e. D row has been me...

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