Hey John,

Before attempting to answer, I would like to clarify the question details. See below:

1. So Discount rate is 10%?

2. Growth rate is 5% but growth starts in year 1. I.e. Yr. 2 realized amount= PMT*(1.05)?

3. The limit on error is -/+250k?

If so, the best way will be to draw a timeline to get an idea of what you working with, see below:

Yr. (0) = -PMT0 (you make the investment) i.e. beginning of Yr.1 you make an investment hence (–PMT). This is already yr. zero dollars so no need for discounting

Yr. (1) = +PMT1/ (1.1) ^1 (so first return payment made at end of yr.1 discounted to time zero)

Yr. (2) = +PMT2/ (1.1) ^2 (so second return payment, made at end of yr.2 and grown at 5% then discounted to time zero) Note: PMT2= (+PMT1*1.05)

Yr. (3) = +PMT3/ (1.1) ^3(so third return payment, made at end of yr.3 and grown at 5% then discounted to time zero) Note: PMT3= (+PMT2*1.05)

Now the difficult part becomes what the PMT values are, if you have a number that can be easily square or cube rooted, then taking the square root and cube root first, and then dividing and finally squaring and cubing post division would be way better than long division route.

Also note that I rounded the top and bottom in yr2 and yr3 for ease (have to round smartly here, rounding both numbers to easy to divide numbers without inflating them, in this case I round them both down). After all you have an error budget of about 250k and this allows you to be in range:

Yr.0=-2809

Yr.1= 1000k/1.1=+909

Yr.2= sqrt[1050k/1.1^2] ~ 30/1.0= 30^2 = 900

Yr.3= Cubert[1103k/1.1^3] ~ 10/1.0= 10.33^3=+1000

Npv=0

Exact calculation

Yr.0=-2809

Yr.1= 909

Yr.2= 867

Yr.3= 828.7

NPV= -204.3k less than or within -/+250k budget

Hope this helps.