Find the present value of 300 pounds paid every 3 years

Question

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 06 '19 at 18:23

score 1 · Answer 1 · answered Mar 06 '19 at 18:14

1

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

answered Mar 06 '19 at 18:14

uniquesolution

18,541

Can you explain me why my method is wrong tho? – Mar 06 '19 at 18:42
Your method is wrong because delayed periodic instalments of 300 is NOT the same as 100 paid for 45 years in arrears. – uniquesolution Mar 06 '19 at 18:49
If it wasn't delayed, would my method have been correct? – Mar 06 '19 at 19:00

Find the present value of 300 pounds paid every 3 years

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