Question

-Which one of the following statements concerning interest rates is correct?  

A.	Savers would prefer annual compounding over monthly compounding.

B.	The effective annual rate decreases as the number of compounding periods per year increases.

C.	The effective annual rate equals the annual percentage rate when interest is compounded annually.

D.	Borrowers would prefer monthly compounding over annual compounding.

E.	For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate.

-Nick got a $125 a month for four years while attending college to earn his undergraduate degree. At a 6.5 percent discount rate, what were these payments worth to him on the day he started college.

A.

$5,201.16

B.

$5,270.94

C.

$5,509.19

D.

$5,608.87

E.

$5,800.00

-You just won a lottery. You have two options for receiving the  proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. You can earn 6 percent on your money. Which option should you take and why?

A.	You should accept the payments because they are worth $209,414 to you today.

B.	You should accept the payments because they are worth $247,800 to you today.

C.	You should accept the payments because they are worth $336,000 to you today.

D.	You should accept the $200,000 because the payments are only worth $189,311 to you today.

E.	You should accept the $200,000 because the payments are only worth $195,413 to you today.

-Lori is considering an annuity, which costs $160,000 today. The annuity pays $17,500 a year at an annual interest rate of 7.50 percent. What is the length of the annuity time period?

A.

13 years

B.

14 years

C.

15 years

D.

16 years

E.

17 years

Answer 1

1]

(a) is incorrect.

Savers would prefer more frequent compounding as the future value of their savings would be higher with more frequent compounding

Future value = present value * (1 + (r/n))^n*t

where r = annual percentage rate

n = number of compounding periods per year

t = number of years

(b) is incorrect.

Effective annual rate = (1 + (r/n))ⁿ - 1

where r = annual percentage rate

n = number of compounding periods per year

The effective annual rate increases as the number of compounding periods per year increases.

(c) is correct

Effective annual rate = (1 + (r/n))ⁿ - 1

where r = nominal annual rate

n = number of compounding periods per year

If compounding is annual, then n = 1, and Effective annual rate equals annual percentage rate

(d) is incorrect

Borrowers would prefer less frequent compounding as the amount of interest paid is lower with less frequent compounding.

(e) is incorrect

For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate if and only if the interest is not compounded annually.