SOLUTION: Your business will pay you distributions of $16,000 in 12 months and another $13,000 in 23 months. If the discount rate is 7% per annum (compounding monthly) for the first 15 month

Question 1161011: Your business will pay you distributions of $16,000 in 12 months and another $13,000 in 23 months. If the discount rate is 7% per annum (compounding monthly) for the first 15 months, and 9% per annum (compounding monthly) for the next 8 months, what single amount received today would be equal to the two proposed payments?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
they are going to pay you 16000 in 12 months and another 13000 in 23 months.
the discount rate is 7% per year compounded monthly for the first 15 months and 9% per year compounded monthly for the next 8 months.
the monthly interest rate for the 7% per year is equal to .07/12.
the monthly interest rate for the 9% per year is equal to .09/12.
you will be using the rate, not the percent.
the rate is the percent divided by 12.
the present value of 16000 from time period 12 to time period 0 is equal to 16000 / (1 + .07/12) ^ 12.= = 14921.33545. *****
the present value of 13000 from time period 23 to time period 15 is equal to 13000 / (1 + .09/12) ^ 8 = 12245.68021.
the present value of 12245.68021 from time period 15 to time period 0 is equal to 12245.68021 / (1 + .07/12) ^ 15 = 11222.57595. *****
that would give you a combined present value of 14921.33545 + 11222.57595 = 26143.9114.
that's your answer.
the attached spreadsheet shows the calculations to find the present values and also shows the cash flow analysis that confirms that the solution is correct.
to prove the calculations are correct, i created a balance sheet with the present value as the initial remaining balance.
i then calculated the remaining balance for the next 23 months using 7% compounded monthly for the first 15 monthsw and 9% compounded monthly for the remaining 8 months.
the calculations showed that the combined present value was correct.
here's what the calculations looked like.

your solution is 26143.91 rounded to 2 decimal places.

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