## The Dependence of Property Value on Interest Rates

As interest fall, it becomes more attractive to hold physical assets, which tend to hold their values against financial assets better the lower interest rates are. If the physical assets also attracts a rental income - such as property, then its value can rise even more. To see why this is so, we can analyse the discounted future income - that is the total present value of future income taking account of assumed future interest rates.Suppose the interest rate is

\[r\]

and the rent is fixed at £10,000 paid once a year in advance. At the start of the second year £10,000 is paid. Because the property owner must wait a year and could invest the money at an interest rate of \[r\]

% the money is only worth £\[10,000/1.0r\]

now.At the start of the third year £10,000 is paid. Because the property owner must wait two years and could invest the money at an interest rate of

\[r\]

% the money is only worth £\[\10,000/(1.0r)^2\]

now.Continuing in this way, the total value of all future income at this interest rate is

\[I=10000+10000/1.0r+10000/(1.0r)^2 +....\]

This is a geometric series with first term

\[a=10000\]

and common ratio \[r= 1/1.0r\]

.The sum of a geometric series with first term

\[a\]

and common ratio \[r\]

is \[S= \frac{a}{1-r}\]

Hence

\[I=\frac{10000}{1-1/1.0r}\]

.If

\[r=7 \%\]

then \[I= 10000/(1-1/1.07) =152857\]

If

\[r=2 \%\]

then \[I= 10000/(1-1/1.02) =510000\]

If

\[r=0.05 \%\]

then \[I= 10000/(1-1/1.005) =2910000\]

This calculation ignores rent rises and is why property prices rocket when interest rates fall.