Answer to Question #127386 in Financial Math for Wachira Ann Wangari

Question

A loan is to be repaid by annuity payable annually in arrears.The annuity starts at rate of ksh 300 per annum.The annuity is repaid for 20years and repayment are calculated using a rate of interest of 7%p.a effective calculate
1) The original amount of the loan
2) The capital outstanding immediately after 5th payment had been made
3)The capital and interest components of the 1st payment

Answer 1

a)Original amount of loan

The rate of interest per payment period is 7%

The annual installment is Ksh. 300

There are 20 payments,

300=$(\frac{x(0.07)}{1-(1.07)\def\foo{^{-20}} \foo} )$

$300= \frac{x(0.07) } {1-0.2584}$

0.07x=222.47

x=3,178.20

=Ksh.3,178.20

b) $=300×(\frac{(1+0.07)\def\foo{^{-5}} \foo} {0.014})$

=Ksh.1,230.06

Capital outstanding =(3,178. 20--1,230.06)

=Ksh.1,948.14

c)=$300×(\frac{(1+0.07) \def\foo{^{-19}} \foo } {0.07})$

=Ksh. 3,100.68

=3178.20-3,100.68

=Ksh. 77.52

Capital Component =Ksh.77.52

Interestcomponent=3,178.20×0.07=Ksh.222.47