A property is mortgaged over $20$ years at an interest rate of $5.6$% per annum compounded annually. If the mortgage is £$120,000$, what are the annual repayments if payments are made at the end of the year?
Just trying to help someone out with this. I have never done stuff like this but is it like this:
$120000 \times1.056^{20}=A$ (say) and then $A/20$?
Sorry if this is the wrong section to put this in.
You are given a loan (mortgage) with value $L$, and you are expected to pay this back in $N$ years with $i$% interest compounding yearly. So the future payments made in each year $k$ are going to be worth the value of $1$ payment $X$ but discounted due to the time value of money to be: $X\cdot (1+i)^{-k}$. So you need to solve the following: $$L = \sum_{k=1}^NX(1+i)^{-k} = X\sum_{k=1}^N(1+i)^{-k}=X\left[\frac{1-(1+i)^{-N-1}}{1-(1+i)^{-1}}-1\right]$$
Now solve for $X$.
