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	6.58	%
b.	Semiannual payments	6.48	%
c.	Quarterly payments	6.42	%
d.	Monthly payments	6.39	%

Answer 1

Effective interest rate = (1 + r / m )n - 1

where,

r = annual nominal rate

m = compounding periods in a year

n = number of compounding periods

(a) Annual Payment

Since the interest is compouded only once, the interest rate is the annual rate.

Rate=520 / 7900 = 6.58 %

(b) Semi annual payment

Effective interest rate = (1 + r / m )n - 1

r = 0.0658

m= 2

n = 2

Effective interest rate = ((1 + 0.0658 / 2 )2 - 1 ) * 100

= 6.688 %

(c) Quarterly payments

Effective interest rate = (1 + r / m )n - 1

r =0.0658

m= 4

n =4

Effective interest rate = ((1 + 0.0658 / 4 )4 - 1 ) * 100

= 6.74 %

(d) Monthly Payments

Effective interest rate = (1 + r / m )n - 1

r = 0.0658

m= 12

n = 12

Effective interest rate = ((1 + 0.0658 / 12 )12- 1 ) * 100

= 6.78 %