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Sagot :
Answer:
APR = 6.5%
Explanation:
If Kita makes 12 payments of $266.22, the maturity value of the loan will be equal to:
V = 12 x $266.22 = $3194.64
On the other hand, the maturity value is equal to:
[tex]V=P(1+r\cdot t)[/tex]Where P is the initial amount, r is the Annual Percentage Rate APR and t is the time in years. So, replacing V by $3194.64, P by $3000, and t by 1 year (12 months), we get:
[tex]\begin{gathered} 3194.64=3000(1+r\cdot1) \\ 3194.64=3000(1+r) \end{gathered}[/tex]Now, we can solve for r as:
[tex]\begin{gathered} \frac{3194.64}{3000}=\frac{3000(1+r)}{3000} \\ 1.065=1+r \\ 1.065-1=1+r-1 \\ 0.065=r \end{gathered}[/tex]So, the annual percentage rate is 0.065 or 6.5%
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