20. Growing annuities certain period of time. However, not all annuities are created equal. Some Annuities are a series of constant cash flows that have been received over annuities adjust the payments based on certain macroeconomic factors. Growing annuities are series of payments that grow at a rate. You invested in an aggressive growth fund and expect to earn 19.08% annually over the next five years. However, due to strong growth, inflation is expected to be 9.45%. What should be your expected real rate of return? 8.80% 9.68% 10.56% 6.60% Excel Online Structured Activity: Required annuity payments Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $55,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $50,000 saved, and he expects to earn 7% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent. $ Open spreadsheet a. Complete an amortization schedule for a $39,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 6% compounded annually. Round all answers to the nearest cent. Repayment Ending Beginning Balance Year Payment Interest of Principal Balance 1 $ $ $ $ $ 2 $ $ $ $ $ 3 $ $ $ $ $ b. What percentage of the payment represents interest and what percentage represents principal for each of the three years? Round all answers to two decimal places. % Interest % Principal Year 1: % % Year 2: % % Year 3: % % c. Why do these percentages change over time? 1. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance declines. II. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance declines. III. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance increases. IV. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance increases. V. These percentages do not change over time; interest and principal are each a constant percentage of the total payment. Excel Online Structured Activity: Required Annuity Payments Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires - that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $45,000 has today. He wants all his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 3% per year from today forward. He currently has $125,000 saved and expects to earn a return on his savings of 10% per year with annual compounding. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet How much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) Do not round intermediate calculations. Round your answer to the nearest dollar. $ Excel Online Structured Activity: Loan Amortization Your company is planning to borrow $2.25 million on a 5-year, 14%, annual payment, fully amortized term loan. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet What fraction of the payment made at the end of the second year will represent repayment of principal? Do not round intermediate calculations. Round your answer to two decimal places. % Excel Online Structured Activity: Interest rate premiums A 5-year Treasury bond has a 4.45% yield. A 10-year Treasury bond yields 6.3%, and a 10-year corporate bond yields 8.95%. The market expects that inflation will average 3.75% over the next 10 years (IP 10 = 3.75%). Assume that there is no maturity risk premium (MRP = 0) and that the annual real risk-free rate, r*, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.) A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet What is the yield on this 5-year corporate bond? Round your answer to two decimal places. % Excel Online Structured Activity: Interest Rate Sensitivity A bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediately after she purchased the bonds, interest rates fell to 7%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. X Open spreadsheet What is the percentage change in the price of each bond after the decline in interest rates? Assume annual coupons and annual compounding. Fill in the following table. Do not round intermediate calculations. Round your answers to two decimal places. Price @ 8% Price @ 7% Percentage Change $ $ % % 10-year, 10% annual coupon 10-year zero 5-year zero 30-year zero $100 perpetuity % % %