Question

Suppose you will receive $17,000 in 7 months and another $11,000 in 21 months. If the discount rate is 7% per annum (compounding monthly) for the first 10 months, and 14% per annum (compounding monthly) for the next 11 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

PV of 17000 in 7 months -

n = 7 months

i = 7% per annum or 0.583% per month

FV = 17000

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PV of 11,000 shall be conputed in 2 steps.

PV of 11,000 received at the end of 21 at end of 10 month is,

n = 11 months (21-10)

i = 14% per annum or 1.167% per month

FV = 11,000

PV of 9168 today shall be,

n = 10 months

i = 7% per annum or 0.583% per month

FV = 9168

So, PV of two payments = 8650 + 16322 = 24,972

So, 24,972 received today will be equal to the pv of 2 payment.