Revision as of 14:10, 19 November 2023 by Admin (Created page with "'''Solution: A''' Let K be the amount that Bank B paid. Equating the amount borrowed (the 16 payments discounted at 7%) to the actual payments received (using the 6% yield rate) gives the equation <math display="block"> 1000 a_{\overline{1677 \%}}=1000 a_{\overline{8} | 6 \%}+\frac{K}{1.06^8} . </math> Then, <math display="block"> \begin{aligned} K & =1000\left(a_{\overline{16} |7 \%}-a_{\overline{8} \mid 6 \%}\right) 1.06^8 \\ & =1000(9.44665-6.20979) 1.06^8 \\ &...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: A
Let K be the amount that Bank B paid. Equating the amount borrowed (the 16 payments discounted at 7%) to the actual payments received (using the 6% yield rate) gives the equation
[[math]]
1000 a_{\overline{1677 \%}}=1000 a_{\overline{8} | 6 \%}+\frac{K}{1.06^8} .
[[/math]]
Then,
[[math]]
\begin{aligned}
K & =1000\left(a_{\overline{16} |7 \%}-a_{\overline{8} \mid 6 \%}\right) 1.06^8 \\
& =1000(9.44665-6.20979) 1.06^8 \\
& =3236.86(1.59385)=5159.06 .
\end{aligned}
[[/math]]
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