Question

For questions 1 - 4 use a required nominal annual return: I jus finished this homework, and i wanted to know wheter my answers were correct or no?			5.00%
1. Consider a 1-year CD.		Principal value	$5,000.00
What is the future value of the CD in 1 year AND what is the effective annual rate?
		Future Value	EFF
a. annual compounding?		$5,250.00	5.00%
b. semi-annual compounding?		$5,253.13	5.06%
c. quarterly compounding?		$5,254.73	5.09%
d. monthly compounding?		$5,255.81	5.12%
e. daily compounding?		$5,256.34	5.13%
2. Rework problem #1 assuming a 5-year CD with $5000 principal.
		Future Value	EFF
a. annual compounding?		$6,381.41	5.10%
b. semi-annual compounding?		$6,400.42	5.11%
c. quarterly compounding?		$6,410.19	5.12%
d. monthly compounding?		$6,416.79	5.12%
e. daily compounding?		$6,420.02	5.13%
3. Assume you want to invest $1000 at the END of every year for the next 5 years.
			Future Value
a. What is the future value in year 5, if interest is compounded annually?			$5,536.79
b. What is the future value in year 5 if interest is compounded semiannually?			$12,645.03
4. Rework question 3, assuming payments are made at the BEGINNING of each period.
			Future Value
a. What is the future value in year 5, if interest is compounded annually?			$5,819.22
b. What is the future value in year 5 if interest is compounded semiannually?			$13,291.70

Answer 1

Principal value	5000
Interest rate	5%

Question 1

Period ( in years) - 1

a. Annual compounding

Compounding frequency	1
No. of compounding periods	1
Interest rate	5%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+5%)^1
Future value	5,250.00

Effective annual interest rate	(1+interest rate)^compounding frequency -1
Effective annual interest rate	((1+5%)^1)-1
Effective annual interest rate	5.0000%

b. Semi-annual compounding

Compounding frequency	2
No. of compounding periods	2
Interest rate	2.5000%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+2.5%)^2
Future value	5253.13

Effective annual interest rate	(1+interest rate)^compounding frequency -1
Effective annual interest rate	((1+2.5%)^2)-1
Effective annual interest rate	5.0625%

c. Quarterly compounding

Compounding frequency	4
No. of compounding periods	4
Interest rate	1.2500%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+1.25%)^4
Future value	5,254.73

Effective annual interest rate	(1+interest rate)^compounding frequency -1
Effective annual interest rate	((1+1.25%)^4)-1
Effective annual interest rate	5.0945%

d. Quarterly compounding

Compounding frequency	12
No. of compounding periods	12
Interest rate	0.4167%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+0.4167%)^12
Future value	5,255.83

Effective annual interest rate	(1+interest rate)^compounding frequency -1
Effective annual interest rate	((1+0.4167%)^12)-1
Effective annual interest rate	5.1166%

e. Daily compounding

Compounding frequency	365
No. of compounding periods	365
Interest rate	0.0137%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+0.0137%)^365
Future value	5,256.36

Effective annual interest rate	(1+interest rate)^compounding frequency -1
Effective annual interest rate	((1+0.0137%)^365)-1
Effective annual interest rate	5.1273%

Question 2

Principal value	5000
Interest rate	5%
Period (in years)	5

a. Annual compounding

Compounding frequency	1
No. of compounding periods	5
Interest rate	5.0000%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+5%)^5
Future value	6,381.41

b. Semi - Annual compounding

Compounding frequency	2
No. of compounding periods	10
Interest rate	2.5000%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+2.5%)^10
Future value	6,400.42

c. Quarterly compounding

Compounding frequency	4
No. of compounding periods	20
Interest rate	1.2500%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+1.25%)^20
Future value	6,410.19

d. Monthly compounding

Compounding frequency	12
No. of compounding periods	60
Interest rate	0.4167%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+0.4167%)^60
Future value	6,416.92

e. Monthly compounding

Compounding frequency	365
No. of compounding periods	1825
Interest rate	0.0137%

Future value	Principal value x (1+interest rate)^no. compounding periods
Future value	5000 x (1+0.0137%)^1825
Future value	6,420.18

Unable to provide the complete answer on account of space constraint.