Answer to Question #195588 in Financial Math for Sasah Solomon

Question

A loan of 15,000 is repaid by level repayments at the end of each month for 8 years. The effective annual rate of interest is 5%. Calculate:

a) The monthly repayment.

b) The capital outstanding at the end of the fourth year after the repayment has been made.

c) The interest and capital components of the 49th

instalment.

Answer 1

effective annual rate of interest:

$r_1=(1+r)^{12}-1=0.05$

 interest rate per period:

$r=1.05^{1/12}-1=0.0041$

a)

monthly repayment:

$R=\frac{Pr}{1-(1+r)^{-n}}=\frac{15000\cdot0.0041}{1-1.00041^{-96}}=190.31$

b)

capital outstanding at the end of the fourth year:

$BAL=15000(1+0.0041)^{48}-\frac{190.31((1+0.0041)^{48}-1)}{0.0041}=18255.16-10073.00=8182.16$

c)

interest component of the 49th instalment:

$INT=BAL\cdot0.0041=8182.16\cdot0.0041=33.55$

capital component of the 49th instalment:

$PRN=R-INT=190.31-33.55=156.76$