1. 5.11 Loan Repayments (1/3)
A loan is taken out for $ at 7.2% p.a. over 30 years.
What is the monthly repayment (M)?
Months = 30 yrs x 12 = 360 months
Months Interest = 7.2% p.a. ÷ 12 = 0.6% monthly
For Month 1:
A1 = (1.0061) - M
For Month 2:
A2 = A1 (1.0061) - M
A2 = [ (1.0061) – M] (1.0061) - M
= (1.0062) – M(1.0061) - M
= (1.0062) – M( )

2. 5.11 Loan Repayments (2/3) For Month 3: A3 = A2 (1.0061) - M
A3 = [ (1.0062) – M( )](1.0061) - M
= [ (1.0063) – M( ) - M
= [ (1.0063) – M( )
For Month 360 ($0):
A360= ( )
– M( … ) = 0
M( … ) =
= ( )
M = ( ) ÷ ( … )

3. 5.11 Loan Repayments (3/3)
GP = …
a(rn – 1)
a = 1
n = 360
r = 1.006
Sn =
r – 1
a(rn – 1)
– 1
S360 = =
r – 1
0.006 x …
M =
– 1
0.006
= x ÷
x x 0.006 =
= $