Question

 Suppose that the monthly compounded annual interest rate is 2.5%. What is the [2] present value β of 1 pound received in 1 month from today (in other words, the discounting factor)? Give your answer to 6 decimal places

Answer 1

In this case, we need to determine the monthly effective rate first. After that, we need to calculate the discounting factors that bring the future value of pound 1 in today's value. 

Calculating the monthly effective rate (r):

$r=\frac{i}{m}\\=\frac{0.025}{12}\\=0.0020833333 \space or \space 0.20833333\%$

Where:

The nominal annual interest rate (i) is 2.5% or 0.025,

The number of compounding per year (m) is 12.

Calculating the discounting factor using the present value:

$Present \space value=\frac{FV}{(1+r)^n}\\=\frac{ 1}{(1+0.0020833333)^1}\\= 0.997921$

Where:

The future value (FV) is 1,

The monthly rate (r) is 0.0020833333,

The number of monthly periods (n) is 1. 

Thus, the present value (discounting factor) is 0.997921.