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For questions 1 - 4 use a required nominal annual return: I jus finished this homework,...

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

Solutions

Expert Solution

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.


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