Question

Barcain Credit Corp. wants to earn an effective annual return (EAR) on its consumer loans of 16 percent per year. If the bank uses daily compounding on its loans, what APR is the bank required by law

Answer 1

14.84%

Step-by-step explanation:

The formula to calculate the effective annual return ((EAR) is

Effective annual return (EAR) = {1 + ( r / m) ^m -1}

m = 365 compounded daily for a year

EAR = 0.16

Calculation of APR is as follows

APR = m {( 1 + EAR) ^( 1/m) - 1} ×100

APR = 365 {( 1 + 0.16) ^( 1/365) - 1} ×

APR = 365{(1.16)^(0.00273972603)-1}×100%

APR = 365{1.00040671284 - 1} ×100%

APR = 365× (0.00040671284)×100%

APR = 0.1484× 100%

APR = 14.84%

Answer 2

14.84%

Step-by-step explanation:

Effective annual return (EAR) = (1 + ( r / m) ^m -1

APR = m (( 1 + EAR) ^( 1/m) - 1)

where m = 365 since it is compounded daily

APR = 365 (( 1 + 0.16) ^( 1/365) - 1) = 14.84%