Find the present value of 300 pounds paid every 3 years

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?

• $\dfrac{300}{1.07^2} \times \dfrac{1-1.07^{-3 \times 15}}{ 1-1.07^{-3}} \approx 1358.478469$ – Henry Mar 6 at 18:23
• What formula is that? – Flea Mar 6 at 18:28
• Geometric series – Henry Mar 6 at 18:29
• And would you mind explaining why my method is wrong? – Flea Mar 6 at 18:41
• You have not said what answer you found initially – Henry Mar 6 at 21:41

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 $$300\times\sum_{k=0}^{14}(1.07)^{-2-3k}=1358.48$$