Return of capital sinking fund

[logicandtruth]

Hi All - Would appreciate some help on this please.

Query on level annuities

Q. What is the present value of an investment with an annual income of £10,000 over the next for years at a return of 5% per annum?

A - first image below. I appreciate that the second equation though gives the same correct answer of £35,460, it would be used if the remunerative and accumulative rates were different.

The below image provides a return on and of capital broken down year-by-year. Please could you advise how the figures in the column titled 'return of capital (sinking fund)' are calculated

 

[jvicens]

?

Hi there,

To calculate the present value of an investment with an annual income of £10,000 over the next four years at a return of 5% per annum, you can use the following formula:

PV = C x ((1-(1+r)^-n)/r)

Where:
PV = Present value
C = Annual income
r = Return rate
n = Number of years

In this case, the present value would be £10,000 x ((1-(1+0.05)^-4)/0.05) = £35,460.

As for the figures in the column titled 'return of capital (sinking fund)', this refers to the amount of money that needs to be set aside each year to ensure that the original investment amount is returned at the end of the four years. This is calculated using the following formula:

R = PV x (r/(1-(1+r)^-n))

Where:
R = Annual return of capital
PV = Present value
r = Return rate
n = Number of years

In this case, the annual return of capital would be £35,460 x (0.05/(1-(1+0.05)^-4)) = £8,865.

I hope this helps clarify the calculations for you. Let me know if you have any further questions. Good luck with your research!