Answer to Question #167485 in Financial Math for kenny dug

Question

A small company is owed the following amounts £5000 on 1 January 2001, £5000 on 1 January 2002 and £10,000 on 1 January 20004. Assuming a constant force of interest of 5% per annum, find the value of the loan on 1 January 2000. What is the value of the loan on 1 July 2001.

Answer 1

a. since the total loan at the beginning of 2004 is 10000, therefore, the present value of the loan is determined using the formula:

$PV=\frac{FV}{(1+\frac{r}{n})^{nt}}$

where PV=present value=10000 ;

i=interest rate=0.05

t=number of years to take into consideration= 5years

n= number of compounding periods of interest per year=1 (annually)

$PV=\frac{10000}{(1+\frac{0.05}{1})^{1*5}}$

PV=7835.261665

the present value of the loan on 1st January, 2000 is 7835 while the future value of the loan on 1st January, 2004 is 10000

b. since the question requires that the value of the loan be calculated for 1st July, 2001 of which the future value for 1st January, 2004 is 10000. therefore the interest is to be compounded semi-annually given as

$PV=\frac{10000}{(1+\frac{0.05}{2})^{2*5}}$

PV=7811.984017

this means that the interest is compounded semi-annually. therefore, the present value of the loan for 1st July, 2001 is 7811.984017