Your best friend wants to help you out in your time of need. She offers you a lo

Question

Your best friend wants to help you out in your time of need. She offers you a loan with an effective annual interest rate of 14 percent What is the equivalent semi-annual (6 month) interest rate on this loan? Note I don't want the APR, I want the EPR (the actual 6 month interest rate) 14.49% What is the quarterly interest rate on this loan? Note I don't want the APR I want the EPR (the actual 3 month interest rate) 1332 0 % Enter as a percent and round to two digits) What is the equivalent 18-month interest rate on this loan? Enter your answer as a percentage rounded to two decimal Note I don't want the APR I want the actual 18-month interest rate 13.69 O % (Enter as a percent and round to two,digits) eBook & Resources it 50

Explanation / Answer

(i)

EAR = 14 %

1/r2 = year

We need to compute EPR1/2

EAR = (1 + EPR1/2)2 – 1

0.14 = (1+ EPR1/2)2 – 1

1 + 0.14 = (1+ EPR1/2)2

1.14 = (1+ EPR1/2)2

(1.14)1/2 = 1+ EPR1/2

EPR1/2 = (1.14)1/2 – 1

EPR1/2 = 1.067707825 – 1

EPR1/2 = 067707825 or 6.77 %

(ii)

EAR = 14 %

1/r4 = year

We need to compute EPR1/4

EAR = (1 + EPR1/4)4 – 1

0.14 = (1+ EPR1/4)4 – 1

1 + 0.14 = (1+ EPR1/4)4

1.14 = (1+ EPR1/4)4

(1.14)1/4 = 1+ EPR1/4

EPR1/4 = (1.14)1/4 – 1

EPR1/4= 1.033299485 – 1

EPR1/4 = 033299485 or 3.33 %

(iii)

EAR = 14 %

1/r1/1.5 = year

We need to compute EPR1.5

EAR = (1 + EPR1.5)1/1.5 – 1

0.14 = (1+ EPR1.5)0.66667 – 1

1 + 0.14 = (1+ EPR1.5)0.66667

1.14 = (1+ EPR1.5)0.66667

(1.14)1/0.66667 = 1+ EPR1.5

EPR1.5 = (1.14) 1.5 – 1

EPR1/1.5 = 1.21718692 – 1

EPR1/1.5 = 0.21718692 or 21.72 %

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