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?

  • $\begingroup$ $\dfrac{300}{1.07^2} \times \dfrac{1-1.07^{-3 \times 15}}{ 1-1.07^{-3}} \approx 1358.478469$ $\endgroup$ – Henry Mar 6 at 18:23
  • $\begingroup$ What formula is that? $\endgroup$ – Flea Mar 6 at 18:28
  • $\begingroup$ Geometric series $\endgroup$ – Henry Mar 6 at 18:29
  • $\begingroup$ And would you mind explaining why my method is wrong? $\endgroup$ – Flea Mar 6 at 18:41
  • $\begingroup$ You have not said what answer you found initially $\endgroup$ – 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 $$300\times\sum_{k=0}^{14}(1.07)^{-2-3k}=1358.48$$

  • $\begingroup$ Can you explain me why my method is wrong tho? $\endgroup$ – Flea Mar 6 at 18:42
  • $\begingroup$ Your method is wrong because delayed periodic instalments of 300 is NOT the same as 100 paid for 45 years in arrears. $\endgroup$ – uniquesolution Mar 6 at 18:49
  • $\begingroup$ If it wasn't delayed, would my method have been correct? $\endgroup$ – Flea Mar 6 at 19:00

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