Find the price which should be paid for an annuity of 500 per year for the next 10 years if the yield rate is to be 11% and if the principal can be replaced by a sinking fund earning 8% per year for the next 6 years and 7% per year for the for the following 4 years after that.
So what I did was:
Given:
annuity of 500 per year for 10 years
yield rate is 11%
sinking fund is 8% for 6 years and then 7% for the following 4 years
so I tried to find the price to be paid:
$$ \frac{P} {s_{10|0.07} - s_{6|0.08}}$$ which I got $\frac {P} {13.81644796 - 7.335929037}$ = $0.15430863P$
but since I want a yield rate of 0.11% I then did $0.11P+0.15430863P=500$ so P=1891.727864
but I am supposed to get the answer to be 2760.22. What am I doing wrong? Thank you
Let be $P=500$, $n=6$, $m=4$, $i=11\%$, $j=8\%$, $k=7\%$.
We have $$ P=P'+P'',\qquad P'=Li,\qquad P''s_{\overline{n}|j}(1+k)^m+P''s_{\overline{m}|k}=L $$ and then $$ L=\frac{P}{i+\frac{1}{s_{\overline{n}|j}(1+k)^m+s_{\overline{m}|k}}}=2760.22 $$