P=principal, n=360 months, i=0.067/12 monthly
The equal monthly payments are:
[tex]A=P\frac{i*(1+i)^n}{(1+i)^n-1}[/tex]
[tex]=P\frac{0.067/12*(1+0.067/12)^{360}}{(1+0.067/12)^{360}-1}[/tex]
=0.0064527798P
Future value of principal after 29 months
F=P(1+i)^29=P(1+0.067/12)^29=1.1752328813 P
Future value of payments after 29 months
[tex]F29=A\frac{(1+i)^n-1}{i}[/tex]
[tex]=A\frac{(1+0.067/12)^{29}-1}{0.067/12}[/tex]
=0.2025204525P
Amount owing after 29 months
=1.1752328813 P - 0.2025204525P
=0.9727124288P
Amount of principal repaid
= P-0.9727124288P
= 0.0272875712P
Portion of payment towards capital (current dollars)
= 0.0272875712P / (29A)
= 0.0272875712/0.1871306136
= 0.14582, or 14.6%
