Question

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 eam interest compounded daily. The annual yield is the rate at which your money earns simple interest in one year. INTEREST EARNED - AMOUNT - ORIGINAL PRINCIPAL INTEREST FOR ONE YEAR PRINCIPAL ANNUAL YIELD - Use the table below to answer the problems. AMOUNT PER $1.00 INVESTED, DAILY COMPOUNDING Annual Interest Period Rate 3 Months One Year 2.5 Years 4 Years 6 Years 5.75% 1.014278 1.059180 1.154458 1.258577 1.411952 6.00% 1.014903 1.061831 1.161820 1.271224 1.433257 6.25% 1.015529 1.084489 1.169103 1.283998 1.454945 6.50% 1.016155 1.067153 1.176431 1.290900 1.478930 6.75% 1.016782 1.009824 1.163806 1.309932 1.499.246 7.00% 1.017408 1.072501 1.191226 1.323094 1.521900 7.25% 1.018036 1.075185 1.198093 1.336389 1.544890 7.50% 1.018663 1.077876 1.206207 1.349817 1.568240 7.75% 1.019291 1.030573 1.213768 1.363330 1.591936 8.00% 1.019920 1.083278 1.221378 1.377079 1.615989 & Years 1.584017 1.616011 1.640651 1.681950 1.715921 1.750579 1.785838 1.822000 1.858306 1.896348 1. Alicia Cox purchased a 21-year certificate of deposit for $15,000. The certificate carns 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 Demaire purchased an 8-year certifionte of deposit for $45.000. The certificate carns interest at 8% compounded daily. a. What is the certificate worth in 8 years! b. What has the certificate eared 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 21-year certificate that earns interest at a rate of 8.00% a. Which certificate offers a higher maturity value? 1. 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 cams Interest at a rate of 1.50% compounded daily? 5. You Invest $25,000 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 1073 City Gene Division

Answer 1

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%iunterest= 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.