Question

If you borrow $7,900 at $520 interest for one year, what is your effective interest rate for the following payment plans? (Input your answers as a percent rounded to 2 decimal places.) Effective Rate of Interest a. Annual payment % b. Semiannual payments % c. Quarterly payments % d. Monthly payments %

Answer 1

For annual payment

A= p*(1+R)^t

A = 7900+520 = 8420

P = 7900

t = 1

8420= 7900*(1+R)^1

(1+R) = 8420/7900 = 1.0658

R = 1.0658- 1 = 0.0658 = 6.58%

EAR = (1+6.58%)-1 = 6.58%

For Semiannual payments

8420= 7900*(1+R/2)^2

(1+R/2)^2 = 1.0658

2+R = ((1.0658)^(1/2))*2

2+R = 2.0648

R = 2.0648-2 = 0.0648 = 6.48%

EAR = ((1+(6.48%/2))^2)-1 = 0.0659 = 6.59%

For quartely payments

8420= 7900*(1+R/4)^4

(1+R/4)^4 = 1.0658

4+R = ((1.0658)^(1/4))*4

4+R = 4.0642

R =4.0642-4 = 0.0642 = 6.42%

EAR = ((1+(6.42%/4))^4)-1 = 0.0658 = 6.58%

For quartely payments

8420= 7900*(1+R/12)^12

(1+R/12)^12 = 1.0658

12+R = ((1.0658)^(1/12))*12

12+R = 12.0639

R =12.0639-12 = 0.0639 = 6.39%

EAR = ((1+(6.39%/12))^12)-1 = 0.0658 = 6.58%