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If you put up $105,000 today in exchange for a 5.375 percent, 15-year annuity, what will...

If you put up $105,000 today in exchange for a 5.375 percent, 15-year annuity, what will the annual cash flow be? Show ALL Work

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Answer #1

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars Amount
PV Annuity $      1,05,000.00
Int Rate 5.3750%
Periods 15

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 105000 / [ 1 - [(1+0.0538)^-180]] /0.0538
= $ 105000 / [ 1 - [(1.0538)^-180]] /0.0538
= $ 105000 / [ 1 - 0.456 ] /0.0538
= $ 105000 / [0.544 / 0.0538 ]
= $ 105000 / 10.1215
= $ 10373.97

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