Question

20) A financial company offers loans to its borrowers at an annual interest rate of 16% compounded quarterly. What is the effective annual interest rate on these loans? What is the EAR if the interest was compounded monthly? Compounded daily?

Answer 1

Q20) i) compounded Quaterly

EAR = ( 1+ R/n) ^n - 1

= ( 1+ 0.16/4)^4 - 1

= ( 1+ 0.04 )^4 - 1

= (1.04)^4 - 1

= 1.16986 - 1

= 0.16986 or 16.986%

ii) Compounded monthly

EAR = ( 1+ R/n)^n - 1

= (1+ 0.16 / 12)^12 -1

= ( 1 + 0.01333)^12 - 1

= (1.01333)^12 - 1

= 1.17222 - 1

= 0.17222 or 17.22%

iii) Compounded daily

EAR = (1+ R/n)^n - 1

= ( 1+ 0.16/365)^365 -1

= (1+0.000438356)^365 - 1

= (1.000438356)^365 - 1

= 1.17347 - 1

= 0.17347 or 17.347%