The problem asks us to calculate the present value ($PV$) of a guaranteed promise of £10000 payable in ten years, given an interest rate of 4.5%. The formula to use is presented in the image: $PV = \frac{FV}{(1+i)^n}$ where $FV$ is the future value, $i$ is the interest rate, and $n$ is the number of years.

1. Problem Description

The problem asks us to calculate the present value ($PV$) of a guaranteed promise of £10000 payable in ten years, given an interest rate of 4.5%. The formula to use is presented in the image:

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

where $FV$ is the future value, $i$ is the interest rate, and $n$ is the number of years.

2. Solution Steps

We are given:

$FV = 10000$

$i = 4.5\% = 0.045$

$n = 10$

Plugging these values into the formula:

$PV = \frac{10000}{(1+0.045)^{10}}$

$PV = \frac{10000}{(1.045)^{10}}$

$PV = \frac{10000}{1.55296942}$

$PV \approx 6439.2769$

Therefore, the present value is approximately £6439.

2

8.

3. Final Answer

£6439.28