Math Is Fun Forum

pletharoe

Member

Registered: 2014-11-15

Posts: 2

Advanced compound interest problem

Hi all,

I want a single expression to calculate total house rental income over a period of years.

x = house price increase per year (as a factor of price)
y = rental yield per year (multiply house price by y to get total rent paid in that year)

So if the house price is $100,000, x = 0.05 and y = 0.05
Year 1
Value: $100,000
Rental yield: $5,000

Year 2
Value: $105,000
Rental yield: $5,250

Year 3
Value: $110,250
Rental yield: $5,512.50

Total rent after 3 years = $15,762.50

Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Advanced compound interest problem

hi pletharoe,

Welcome to the forum.

If I use P for the initial value of the house then the new value after n years is given by the standard compound interest formula:

If I've understood you correctly, the rent is found by multiplying this value by y.  And it's y every year. So the rental is given by

This is a geometric series, with first term Py, and common ratio (1+x), so using the sum of such a series we get

Let's check it out with your figures:

That looks good to me. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

pletharoe

Member

Registered: 2014-11-15

Posts: 2

Re: Advanced compound interest problem

Thanks very much Bob, that's exactly what I was looking for.