SOLUTION: What is the present value of 10 semi-annual payments of 2,000 pesos each if the first payment is due at the end of 3 years and money is worth 8% compounded quarterly?

Question 1188286: What is the present value of 10 semi-annual payments of 2,000 pesos each if the first payment is due at the end of 3 years and money is worth 8% compounded quarterly?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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 https://arachnoid.com/finance/index.html

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.

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.

let me know if you have any questions.

theo

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