Mortgage Math () - University of Kentucky
Mortgage Math
?What is PV of $1000 per month for 15 months plus $10,000 paid 15 months from now at 10% nominal annual interest?
$22,875 = $1,000 + L + $1,000 + $10,000
1 + .10 12
(1 + .10 12)15
(1 + .10 12)15
= (14.045)1000 + (0.8830)10000
= $14,045 + $8,830
= (PVIFA.00833,15)*PMT + (PVIF.00833,15)*FV
(With calculator set to pmts at "END" of periods, and P/YR=12...)
Mortgage Math Keys:
DCF Keys:
15----> N key
10----> I/YR key
10----> I/YR key
0 ----> CFj key
1000 ----> PMT key
1000----> CFj key
10000----> FV key
14 ----> Nj key
PV ----> -22,875
11000---->CFj key
NPV ----> 22,875
How the Calculator "Mortgage Math" Keys Work. . .
The five "mortgage math" keys on your calculator (N,I,PV,PMT,FV) solve:
0 = - PV
+
PMT 1+ r
+
PMT
(1 + r)2
+L+
PMT
(1 + r)N
FV +
(1 + r)N
or:0 = -PV + (PVIFAr,N)*PMT + (PVIFr,N)*FV
where: r = i / m,
where: i = Nominal annual interest rate
m = Number of payment periods per year (m?P/YR).
Example:
10%, 20-yr fully-amortizing mortgage with payments of $1000/month.
The calculator solves the following equation for PV:
0
=
-PV
1000 +
1.00833
+
1000
(1.00833)2
+L+
1000
(1.00833)240
+
0
(1.00833)240
The result is: PV = 103625.
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