Using an interest rate of 7% per annum, find the present value of fifteen payments of amount £300 each payable every three years, with the first payment made at the end of the second year
I thought this as equal to an annuity of 100 pounds payable in arrears r for 45 years discounted back by v^1 at 7% because it is starting at the end of year 2. but I get the wrong answer as it should be 1358.48. Can someone explain me why my method is wrong?
Let $p_t$ denote the payment at future time $t$. Then the future payments are $p_2,p_5,\dots,p_{44}$, or $p_{2+3k}$ where $k=0,1,\dots 14$. The present value of $p_{2+3k}$ is $\frac{300}{(1+0.07)^{2+3k}}$, hence the present value of the entire cashflow is $$300\times\sum_{k=0}^{14}(1.07)^{-2-3k}=1358.48$$