Is the answer correct? if yes, would you please explaine the highlighted numbers

Question

Is the answer correct? if yes,

would you please explaine the highlighted numbers in yellow and pink? (should I just subtract one from the original value?)

I also highlighted number 6 (in green).. why did we choose this number?

this equation could be useful

Problem 3: (25 points) Assume that you have payments of2.000 QAR in year three and increasing by 5% per year through year 8. Find the equivalent uniform payments in years five through eight at an interest rate of 10% per year Answer: Compute the Pg in year 2 Pg--2.000* { 1-[( 1 + 0.05)/( 1 + 0. I 0)19 /(0. I 0-0.05)--9.742.04 Pg 9,742.04 in year 2 should be converted to year 4(F/P,10%,2) Py-9,742.04 (1.21)--11,787.87 Then, A-PAP. 10%,4)--11 ,78 7.87 (0.31 547)--3,7 18.72

Explanation / Answer

Your answer, 3718.50 is correct.

The question says payment of 2000 is in year 3 and payments continue till year 8 with 5% increase every year. So, effectively payments have to brought to year 0 (i.e. today), to do so we are discounting payments of 6 years ( no of payments) for 8 years (span of investment) (because year 1 and year 2 have no payments)

In the given solution, Present value of 6 payments is calculated at the end 2nd yaers is calculated. then the resultant value is again discounted for 2 yaers to bring it to year 0 (which is termed in solution as bring year 2 to year 4).

The Ultimate present value of payments is divided by the sum of pv factors for years 4 to 8 @ 10%.

I am giving you the excel answer for better understnding.

Please comment for any further explanation.

Year Cashflow Present value@10% Discounted cashflow 1 0 0.909 0.00 2 0 0.826 0.00 3 2000.00 0.751 1502.00 4 2100.00 0.683 1434.30 5 2205.00 0.621 1369.31 6 2315.25 0.564 1305.80 7 2431.01 0.513 1247.11 8 2552.56 0.467 1192.05 Present value 8050.56 Anuity factor from Year 5 to 8 2.165 Equal annual payments 3718.50

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