Question 1188286
the interest rate per semi-annual period is calculated as follows:


8% / 4 = 2% per quarter.
1.02^2 = 1.0404 - 1 = .0404 * 100 = 4.04% per semi-annual time period.


present value of 10 semi-annual payments of 2000 each is equal to 16,189.53796.


the present value of that for an addition 6 semi-annual time periods is equal to 12,765.3402.


your solution is 12,765.34, rounded to the nearest penny.


i used the ti-ba-ii business analyst calculator to get these results.


an online calculator that gives similar results can be found at <a href = "https://arachnoid.com/finance/index.html" target = "_blank">https://arachnoid.com/finance/index.html</a>


the present value from that calculator is 16,189.54.


the present value of that for an additional 6 semi-annual periods is equal to that divided by 1.0404^6 = 12,765.34181.


round to nearest penny to get 12,765.34.


here are the resuls from using that calculator.


<img src = "http://theo.x10hosting.com/2021/120107.jpg" >


i also did an excel analysis to give you the semi-annual period by semi-annual time periods results.


that shows that the present value is 12,765.35.
that grows to 16,189.54 in semi-annual period 6, at which time the payments of 2000 at the end of each semi-annual time period kick in.
the loan terminates in 10 additional semi-annual time periods, when the remaining balance becomes equal to 0.


here's what the excel results look like.


<img src = "http://theo.x10hosting.com/2021/120108.jpg" >


let me know if you have any questions.


theo