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
* 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)
5*
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.