Question

Find the APR, or stated annual rate, in each of the following cases.

Required:

(a)	An effective annual interest of 19% (the APR is compounded semiannually)
	(Click to select)  17.27%  18.17%  15.45%  19.90%  16.36%

(b)	An effective annual interest of 17% (the APR is compounded monthly)
	(Click to select)  12.64%  15.80%  17.72%  18.96%  18.17%

(c)	An effective annual interest of 15% (the APR is compounded weekly)
	(Click to select)  16.79%  15.56%  11.20%  15.39%  13.99%

(d)	An effective annual interest of 8% with infinite (or continuous) compounding
	(Click to select)  8.47%  7.70%  8.27%  8.16%  6.93%

Answer 1

Solution

a. Effective annual rate=(1+APR/M)^M-1

WHERE

m-number of compounding periods in an year

Putting values

19%=(1+APR/2)^2-1

Solving we get APR=18.17%

b

Effective annual rate=(1+APR/M)^M-1

WHERE

m-number of compounding periods in an year

Putting values

17%=(1+APR/12)^12-1

Solving we get APR=15.80%

c

Effective annual rate=(1+APR/M)^M-1

WHERE

m-number of compounding periods in an year

Putting values

15%=(1+APR/52)^52-1

Solving we get APR=13.99%

d. Effective annual rate=exp^r-1

r-APR

8%=exp^r-1

Solving we get APR=7.70%

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