Answer to Question #172589 in Financial Math for janice

Question

Calculate the present value as at 1 March 2005 of a series of payments of £1,000 payable on the first day of each month from April 2005 to December 2005 inclusive, assuming a rate of interest of 6% pa convertible monthly. 

Answer 1

This requires present value of annual due since it requires payment at the beginning of each period.from the formula below;

P = Total payment from 1/April/2005 to 1/December/2005 which is equal to 9000.

r= rate of interest of 6%

n= number of years which is less than equal to 1

M= number of months compounded which 10 months divided by 12 months

$PVA_{due}= P \times [1-(1+\frac{r}{n})^{-t \times n}] \times [\frac{1+\frac{r}{n}}{\frac{r}{n}}]\\ =9000 \times [1-(1+\frac{0.06}{0.8333})^{-1 \times 0.8333}] \times [\frac{1+\frac{0.06}{0.8333}}{\frac{0.06}{0.8333}}]\\ \implies 7542.824295$

The result shows that the present value of 9000 at the beginning of December 2005 is 7543 as at the beginning of March 2005.