A 20000 bond has annual coupons and is redeemable at the end of fourteen years for 22600. It has a base amount equal to 18450 when purchased to yield 6%. Find its base amount if it were purchased to yield 7%.
I assumed that both bonds would have the same price, and set up the equation $$P = (C-G)v^n_j+G$$ Where C=22600, j=6%, G=18450, and n=14. Plugging that all in gets P=20285.549. Using the same equation, except making j=7% and G to be unknown gets G=18819.35. However the answer appears to be 15814.29. Am I doing a step incorrectly, or just missing something?
$G=20,000$, $F=18,450$, $j=6\%$:
$$ G=\frac{Fr}{j}\qquad\Longrightarrow\qquad r=\frac{Gj}{F}=\frac{20,000\times 0.06}{18,450}\approx 5.535\% $$
If it were purchased to yield $7\%$, we'd had: $$ G=\frac{Fr}{j}=\frac{18,450\times 0.05535}{0.07}\approx 15,814.29 $$