Question

A loan is to be repaid by annuity payable annually in arrears. The annuity starts at rate of Kshs. 300 per annum and increases each year by Kshs. 30 per annum. The annuity is repaid for 20 years and repayments are calculated using a rate of interest of 7% per annum effective. Calculate i) The original amount of the loan [1Mk] ii) The capital outstanding immediately after 5th payment has been made [2Mks] iii) The capital and interest components of the first payment

Answer 1

Given data

Starting Annuity = A' = 300 Kshs

Gradient = G = 30 Kshs

Tenure = n = 20 years

Interest rate = 7%

Solution:

Equal montly installments = [300 + 30(A/G,i,n)]

Equal montly installments = [300 + 30(A/G,7%,20)]

Using DICF tables

Equal montly installments = 300 + 30(7.3163)

Equal montly installments = 519.5 Kshs = 520 Kshs

i) The orignal amount of the loan willl be equal to the Present worth(PW) of the cash flow.

PW = [300 + 30(A/G,i,n)](P/A,i,n)

PW = [300 + 30(A/G,7%,20)](P/A,7%,20)

Using DICF tables

PW = (300 + 30(7.3163))(10.5940)

PW = 5503.5 Kshs = 5504 kshs

ii) The capital outstanding after 5th payment.

In order to find out the same we must know the interest component payed every installment. the same can be found by

Interest component = FW - PW

FW = 520(F/A,7,20)

Using DCIF Tables

FW = 520(40.9955)

FW = 21318 Kshs

Interest component = 21318 - 5504 = 15814

iii) Interest component per installment = [15814/21318]*520 = 386 kshs

iii) Capital component per installment = [5504 / 21318]*520 = 134 kshs

ii)Capital outstanding after 5th payment = 5504 - 5*134 = 4834 kshs