Question

Suppose you will receive $19,000 in 7 months and another $13,000 in 22 months. If the discount rate is 5% per annum (compounding monthly) for the first 10 months, and 10% per annum (compounding monthly) for the next 12 months, what single amount received today would be equal to the two proposed payments? (answer to the nearest whole dollar; don’t include the $ sign or commas)

Answer #1

Solution.>

In this particular question, basically we have to find the sum of the present value of both the amounts. The PV of both the amounts will be equal to the single amount we receive today.

For the $19,000, time period = 7 months and rate = 5%

Present Value = Amount / ( 1+rate/12)^months

Present Value = $19000 / ( 1+5%/12)^7

Present Value = **$18,454.96**

For the $13,000, time period = 22 months and rate = 5% for first 10 months and 10% for next 12 months

Present Value at the end of 10 months = $13000 / ( 1+10%/12)^12

Present Value at the end of 10 months = $11,767.76

Present Value now = Present Value at the end of 10 months / ( 1+5%/12)^10

Present Value now = $11,767.76 / ( 1+5%/12)^10

Present Value now = **$11,288.49**

Total Amount = $18,454.96 + $11,288.49

**Total Amount = $29,743**

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