College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.7 - Financial Models - 6.7 Assess Your Understanding - Page 476: 66


$ r\approx 6.3\%$

Work Step by Step

The present value $P$ of $A$ dollars to be received after $t$ years, assuming a per annum interest rate $r$ compounded $n$ times per year, is $P=A\displaystyle \cdot\left(1+\frac{r}{n}\right)^{-nt}$ --- $A={{\$}} 25,000, P=15,334.65$ $n=1, \mathrm{t}=8.$ $r=?$ $15,334.65=25,000(1+\displaystyle \frac{r}{1})^{-8}\qquad.../\div 25,000$ $\displaystyle \frac{15,334.65}{25,000}=(1+r)^{-8}\qquad.../(....)^{-1/8}$ $\displaystyle \left(\frac{15,334.65}{25,000}\right)^{-1/8}=1+r$ $r=\displaystyle \left(\frac{15,334.65}{25,000}\right)^{-1/8}-1\approx 0.63$ $ r\approx 6.3\%$
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