1



You decide to purchase a building for $30,000 by paying $5,000 down and assuming a mortgage of $25k. The bank offers you a 15-year mortgage requiring annual end-of-year payments of $3188 each. The bank also requires you to pay a 3percent loan origination fee, which will reduce the effective amount the bank lends to you. Compute the annual percentage rate of interest on this loan?     

PVAN0 = $30,000 - $5,000(down) - $750 (loan origination fee)

= $24,250

Origination fee = 0.03 x $25,000 = $750

$24,250 = $3,188(PVIFAi,15)

PVIFAi,15 = 7.607

Therefore, i = 10% from Table IV

2. Construct a loan amortization schedule for a 3-year, 11 percent loan of $30k. The loan requires three equal, end-of-year payments.           

$30,000 = PMT(PVIFA.11,3) = PMT(2.444)

PMT = $12,275

End of Year PMT(Payment) Interest Principal Balance Remaining

0 - - - $30,000

1 $12,275 $3,300 $8,975 21,025

2 12,275 2,313 9,962 11,063

3 12,275 1,217 11,058 5*

* difference from zero due to rounding in tables

                                                 

3. Crab State Bank has offered you a $1,000,000 5-year loan at an interest rate of 11.25 percent, requiring equal annual end-of-year payments that include both principle and interest on the unpaid balance. Develop an amortization schedule for this loan..

$1,000,000 = PMT (PVIFA0.1125, 5)

PMT = $272,274 (by calculator)

|End of |Payment |Interest |Principal |Balance Remaining |

|Year | | | | |

|0 |-- |-- |-- |$1,000,000 |

|1 |$272,274 |$112,500 |$159,774 |840,226 |

|2 |272,274 |94,525 |177,749 |662,477 |

|3 |272,274 |74,529 |197,745 |464,732 |

|4 |272,274 |52,282 |219,992 |244,740 |

|5 |272,274 |27533 |244,741 |-1* |

*Differs from $0 due to rounding.

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