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"Elliott Credit Corp. wants to earn an effective annual return on its consumer loans of 17.1 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers?" (Use 365 days a year. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Respuesta :

TomShelby

Answer:

APR 15.79% compounding daily

Explanation:

The bank will annunce the annual percentage rate which is equivalent to the effecte annual return

[tex](1+apr/m)^m = 1 + r_e\\(1+apr/365)^365 = 1+0.171\\apr = (\sqrt[365]{1.171} -1) \times 365[/tex]

APR = 0.157892225 = 15.79%

amanarsalan

Answer:

15.79%

Explanation:

[tex]r_{e}[/tex] = EAR = [tex](1 + \frac{r}{m}) ^{m} - 1[/tex]

where [tex]r_{e}[/tex] = EAR = Annual Rate of Return = 0.171

m = Number of compounding periods per year = 365

r = APR = ?

[tex]r = APR = m [(1+EAR)^{\frac{1}{m} } -1][/tex]

[tex]r = APR = 365 [(1+0.171)^{\frac{1}{365} } -1][/tex]

[tex]r = APR = 365 [1.00043258 -1][/tex]

[tex]r = APR = 365 [0.00043258][/tex]

[tex]r = APR = 0.15789[/tex]

r = APR = 15.79%

Hence the Interest Rate required by the bank to report to potential borrowers is 15.79%

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