Question

can someone walk me through all the problems?

LESSES 10-6, 108 Certificates of Deposit and Effective Annual Yield Your money earns interest at a higher rate when you buy a certificate of deposit than it does when you invest it in a regular savings account. Most certificates earn interest compounded daily. The annual yield is the rate at which your money earns simple interest in one year. INTEREST EARNED - AMOUNT - ORIGINAL PRINCIPAL ANNUAL YIELD - INTEREST FOR ONE YEAR PRINCIPAL Use the table below to answer the problems. Annual Rate 8 Years 5.75% 6.00% 6.25% 6.50% 6.75% 7.00% 7.25% 7.50% 7.75% 8.00% AMOUNT PER $1.00 INVESTED, DAILY COMPOUNDING Interest Period 3 Months One Year 2.5 Years 4 Years 6 Years 1.014278 1.059180 1.154458 1.258577 1.411952 1.014903 1.061831 1.161820 1.271224 1.433287 1.015529 1.084489 1.169103 1.283998 1.454945 1.016155 1.067153 1.176431 1.296900 1.476930 1.016782 1.069824 1.183806 1.309932 1.499246 1.017408 1,072501 1.191226 1.323094 1.521900 1.018036 1.075185 1.198693 1.336389 1.544896 1.018663 1.077876 1.206207 1.349817 1.568240 1.019291 1.080573 1.213769 1.363380 1.591936 1.019920 1.083278 1.221376 1.377079 1.615989 1.584017 1.616011 1.648651 1.681950 1.715921 1.750579 1.785936 1.822006 1.858806 1.896348 1. Alicia Cox purchased a 23-year certificate of deposit for $15,000. The certificate earns interest at a rate of 7.00% compounded daily. a. What is the amount of the certificate at maturity? b. What is the interest earned? 2. Charles Demaize purchased an 8-year certificate of deposit for $45.000. The certificate earns interest at 8% compounded daily. a. What is the certificate worth in 8 years? b. What has the certificate earned in those 8 years? 3. The Trues have $30,000 they want to invest in a certificate of deposit. They can purchase a 4-year certificate that earns interest at a rate of 5.75% or a 2-year certificate that earns interest at a rate of 8.00% a. Which certificate offers a higher maturity value? b. What is the difference in the maturity values of the two certificates? 4. What is the annual yield on a 1-year $15,000 certificate of deposit that earns interest at a rate of 7.50% compounded daily? 5. You invest S25,000 in an 8-year certificate of deposit that earns interest at 8% compounded daily. What is the annual yield? 6. Most banks pay higher rates of interest for longer periods of deposit. Why? Unit 1973

Answer 1

Note: Details of calculations are given at the end of the answer, a screenshot of Excelsheet.

Part 1:

(a ): Amount at maturity=$17,868.39

(b ): Interest earned= $2,868.39

Part 2:

(a ): Worth of certificate in 8 years= $85,335.66

(b ): Amount earned in 8 years= $40,335.66

Part 3: (a)

Maturity value of 4 year certificate at 5.75%=$37,757.31

Maturity value of 2.5 year certificate at 8%=$36,641.28

Certificate having higher maturity value= 4 year certificate with interest at 5.75%

Part 3 (b):

Difference in the maturity value of the deposits= $1,116.03

Part 4:

Annual yield of 1 year certificate of deposit at 7.5% interest= 0.077876 Or, 7.7876%

Part 5:

Annual yield of 8 year certificate of deposit at 8% interest= 0.112044 Or, 11.2044%

Part 6:

Banks pay higher interest rate for longer term deposits in order to induce depositors to retain the amount with the bank for longer term. Also, the depositors generally required higher interest rate for longer term since the risk involved is higher for longer term deposits, requiring term premium.

Details of calculations as follow:

F A 1 Q# 2 3 1. a and b 4 2. a and b 5 6 7 3 B с D E G Interest rate Period FVIF Deposit Maturity value Interest (Years) (Given) (A) F= A*FVIF I= F-A 7% 2.5 1.191226 15,000 17868.39 2,868.39 8% 8 1.896348 45,000 85335.66 40,335.66 5.75% 4 1.258577 30,000 37757.31 7,757.31 8% 2.5 1.221376 30,000 36641.28 6,641.28 Difference in maturity values= F5-F6 = 1116.03 7.50% 1 1.077876 15,000 16168.14 1,168 Annual Yield=G8/E8 0.077876 8% 8 1.896348 25,000 47408.7 22,409 Annual Yield= (G10/E10)/8 0.112044 8 4 9 10 11 5