Time value of money a. Finding FV Investment (PV) Interest rate) Number of yes INI Future value (FV1 $1,000 ex Formula NNTA Interest Rate (35) 0% 4 4% 25% b. Creating a table with FVs at various interest rates and time periods using Data Table Year (06) Interest Rate (BS) 0% 456 25% 0 1 2 Formulas Year 16) NNA a 1 2 3 4 5 #N/A #NIA #N/A F . F ANTA ANA ENVA ANA ANTA #NA WNA WNA #NA #NA NNA #N/A #NA 4 5 #NIA #N/A Creating a graph with years on the horizontal axis and FV on the vertical axis $1,000 c. Finding PV Future value (FV) Discount rate (1) Number of years INI Dankie BV 6 Formulas WIN armules c. Finding PV Future value (FV) Discount rate (1) Number of years (N) Present value (PV) $1,000 8% 6 Formulas #N/A d. Finding the rate of return provided by the security Cost of security (PV) Future value of security (FV) Number of years (N) Rate of retum (1) $1,000 $3,000 6 #N/A e. Calculating the number of years required to double the population Current population in millions (PV) 35.2 Growth rate (1) 3% Doubled population in millions (FV) #N/A Number of years required to double (N) #N/A f. Finding the PV and FV of an ordinary annuity Annuity (PMT) Interest rate (1) Number of years (N) Present value of ordinary annuity (PV) Future value of ordinary annuity (FV) $1,000 10% 6 #N/A #N/A g. Recalculating the PV and FV for part f if the annuity is an annuity due Present value of annuity due (PV) #N/A Future value of annuity due (FV) #N/A h. Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded Future value (FV) #N/A Present value (PV) #N/A i. Finding the annual payments for an ordinary annuity and an annuity due Present value (PV) $1,000 Discount rate (1) 6% Number of years (N) 12 Annual payment for ordinary annuity (PMT) #N/A Annual payment for annuity due (PMT2) #N/A - Finding the PV and the FV of an investment that makes the following end-of-year payments Year Payment 1 $100 2 S200 3 S500 Interest rate 10 5% Present value of investment (PV) ANA Future value of investment (FV) NA k. Five banks offer the same nominal rate on deposits, but A pays interest annually, B pays semiannually, Cpays quarterly, D pays monthly, and E pays daily. (1) Calculating the effective annual rate for each bank and the future values of the deposit at the end of 1 year and 2 years Nominel rate how Deast PV) $4,500 Number of daya per year 365 Formulas A e FAR FAR FV after 1 year FV after 1 year FV amer 2 years FV after 2 years (2) Calculating the nominal rates that will cause all of the banks to provide the same effective annual rate as Bank A A R C E Nominal rate Nominalnate INN A ANA ENYA #NYA R ANA ANA #NUA C #N/A WNA #NA D B ANA C #NIA D #NA (3) Calculating the amount of payment to be made annually for A, semiannually for B, quarterly for C, monthly for D. and daily for E Nooded amount (FV) $4,500 Number of years (NI 1 D E C Payment (PMT) A #NA B #N'A #NA Payment (PMT) L Setting up the amortization schedule Original amount of mortgage PV) Interest rate) Tem to maturity, years IN S14 000 8% 4 Formula NA Annual payment (PMT) Formulas Beginnine Balance Payment Interest Repayment of Preciaal Ending Balance Year 1 2 3 Year 1 Rapa Beginning Ralanon ANA #NA ANA Payment ANA #N'A ANA Internal WNA #NA 3 Excel Activity: Time value of money The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Do not round intermediate calculations. Enter your answers as positive values. Download spreadsheet Time value of money-cf2963.xlsx a. Find the FV of $1,000 invested to earn 8% after 6 years. Round your answer to the nearest cent. $ b. What is the investment's FV at rates of 0%, 4%, and 25% after 0, 1, 2, 3, 4, and years? Round your answers to the nearest cent. Interest Rate Year 0% 4% 25% 0 $ $ $ 1 $ $ $ 2 $ $ $ 3 $ $ $ 4 $ $ $ 5 $ $ $ Choose the correct graph of future value as a function of time and rate. Note: blue line is for 0%, orange line is for 4%, and grey line is for 25%. The correct graph is 7000 FV as Function of Time and Rate 6000 5000 4000 Future Value (5) A. 3000- 2000- 1000 Year 7000 FV as Function of Time and Rate 6000- 5000 4000 Future Value (S) B. 3000 2000 1000 7000 FV as Function of Time and Rate 6000 5000- 4000 C. Future Value S 3000- 2000 1000 Year 7000 FV as Function of Time and Rate 6000 5000 4000 Future Value (5) D. 3000- 2000 1000 c. Find the PV of $1,000 due in 6 years if the discount rate is 8%. Round your answer to the nearest cent. $ d. A security has a cost of $1,000 and will return $3,000 after 6 years. What rate of return does the security provide? Round your answer to two decimal places. % take for the population to e. Suppose California's population is 35.2 million people, and its population is expected to grow by 3% annually. How long will double? Round your answer to the nearest whole number. years f. Find the PV of an ordinary annuity that pays $1,000 each of the next 6 years if the interest rate is 10%. Then find the FV of that same annuity. Round your answers to the nearest cent. PV of ordinary annuity: $ FV of ordinary annuity: $ g. How will the PV and FV of the annuity in part f change if it is an annuity due rather than an ordinary annuity? Round your answers to the nearest cent. PV of annuity due: $ FV of annuity due: $ h. What will the FV and the PV for parts a and c be if the interest rate is 8% with semiannual compounding rather than 8% with annual compounding? Round your answers to the nearest cent. FV with semiannual compounding: $ PV with semiannual compounding: $ i. Find the annual payments for an ordinary annuity and an annuity due for 12 years with a PV of $1,000 and an interest rate of 6%. Round your answers to the nearest cent. Annual payment for ordinary annuity: $ Annual payment for annuity due: $ j. Find the PV and the FV of an investment that makes the following end-of-year payments. The interest rate is 6%. Year Payment $100 1 2 $200 $500 3 Round your answers to the nearest cent. PV of investment: $ FV of investment: $ k. Five banks offer nominal rates of 4% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. Assume 365 days in a year. 1. What effective annual rate does each bank pay? If you deposit $4,500 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? Round your answers to two decimal places. B D E EAR % % % % % FV after 1 year $ $ $ $ $ FV after 2 years $ $ $ $ $ 2. If the TVM is the only consideration, what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A? Round your answers to two decimal places. B D Nominal rate % % % % 3. Suppose you don't have the $4,500 but need it at the end of 1 year. You plan to make a series of deposits - annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E with payments beginning today. How large must the payments be to each bank? Round your answers to the nearest cent. B D E Payment $ $ $ 4. Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks? It is more likely that an investor would prefer the bank that compounded frequently. I. Suppose you borrow $14,000. The interest rate is 6%, and it requires 4 equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances. Round your answers to the nearest cent. If your answer is zero, enter "O". Beginning Balance Repayment of Principal Ending Balance Year Payment Interest 1 $ $ $ $ $ 2 $ $ $ $ $ 3 $ $ $ $ $ 4 $ $ $ $ Choose the correct graph that shows how the payments are divided between interest and principal repayment over time. The correct graph is Breakdown of payments Breakdown of payments 6000 6000- 5000 5000 4000 4000- Dollar Values 3000 Dollar Values 3000 A. B. 2000- 2000 LII 1000 1000 3 2 3 Year Year Repayment of Principal ($) Interest ($) Repayment of Principal ($) Interest ($) Breakdown of payments Breakdown of payments 6000- 6000- 5000 5000 4000- 4000+ Dollar Values 3000 Dollar Values 3000 C. D. 2000- 2000+ 1000 1000 1 2 3 1 3 Year Year Repayment of Principal ($) Interest ($) Repayment of Principal ($) Interest ($) Check My Work Reset Problem Time value of money a. Finding FV Investment (PV) Interest rate) Number of yes INI Future value (FV1 $1,000 ex Formula NNTA Interest Rate (35) 0% 4 4% 25% b. Creating a table with FVs at various interest rates and time periods using Data Table Year (06) Interest Rate (BS) 0% 456 25% 0 1 2 Formulas Year 16) NNA a 1 2 3 4 5 #N/A #NIA #N/A F . F ANTA ANA ENVA ANA ANTA #NA WNA WNA #NA #NA NNA #N/A #NA 4 5 #NIA #N/A Creating a graph with years on the horizontal axis and FV on the vertical axis $1,000 c. Finding PV Future value (FV) Discount rate (1) Number of years INI Dankie BV 6 Formulas WIN armules c. Finding PV Future value (FV) Discount rate (1) Number of years (N) Present value (PV) $1,000 8% 6 Formulas #N/A d. Finding the rate of return provided by the security Cost of security (PV) Future value of security (FV) Number of years (N) Rate of retum (1) $1,000 $3,000 6 #N/A e. Calculating the number of years required to double the population Current population in millions (PV) 35.2 Growth rate (1) 3% Doubled population in millions (FV) #N/A Number of years required to double (N) #N/A f. Finding the PV and FV of an ordinary annuity Annuity (PMT) Interest rate (1) Number of years (N) Present value of ordinary annuity (PV) Future value of ordinary annuity (FV) $1,000 10% 6 #N/A #N/A g. Recalculating the PV and FV for part f if the annuity is an annuity due Present value of annuity due (PV) #N/A Future value of annuity due (FV) #N/A h. Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded Future value (FV) #N/A Present value (PV) #N/A i. Finding the annual payments for an ordinary annuity and an annuity due Present value (PV) $1,000 Discount rate (1) 6% Number of years (N) 12 Annual payment for ordinary annuity (PMT) #N/A Annual payment for annuity due (PMT2) #N/A - Finding the PV and the FV of an investment that makes the following end-of-year payments Year Payment 1 $100 2 S200 3 S500 Interest rate 10 5% Present value of investment (PV) ANA Future value of investment (FV) NA k. Five banks offer the same nominal rate on deposits, but A pays interest annually, B pays semiannually, Cpays quarterly, D pays monthly, and E pays daily. (1) Calculating the effective annual rate for each bank and the future values of the deposit at the end of 1 year and 2 years Nominel rate how Deast PV) $4,500 Number of daya per year 365 Formulas A e FAR FAR FV after 1 year FV after 1 year FV amer 2 years FV after 2 years (2) Calculating the nominal rates that will cause all of the banks to provide the same effective annual rate as Bank A A R C E Nominal rate Nominalnate INN A ANA ENYA #NYA R ANA ANA #NUA C #N/A WNA #NA D B ANA C #NIA D #NA (3) Calculating the amount of payment to be made annually for A, semiannually for B, quarterly for C, monthly for D. and daily for E Nooded amount (FV) $4,500 Number of years (NI 1 D E C Payment (PMT) A #NA B #N'A #NA Payment (PMT) L Setting up the amortization schedule Original amount of mortgage PV) Interest rate) Tem to maturity, years IN S14 000 8% 4 Formula NA Annual payment (PMT) Formulas Beginnine Balance Payment Interest Repayment of Preciaal Ending Balance Year 1 2 3 Year 1 Rapa Beginning Ralanon ANA #NA ANA Payment ANA #N'A ANA Internal WNA #NA 3 Excel Activity: Time value of money The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Do not round intermediate calculations. Enter your answers as positive values. Download spreadsheet Time value of money-cf2963.xlsx a. Find the FV of $1,000 invested to earn 8% after 6 years. Round your answer to the nearest cent. $ b. What is the investment's FV at rates of 0%, 4%, and 25% after 0, 1, 2, 3, 4, and years? Round your answers to the nearest cent. Interest Rate Year 0% 4% 25% 0 $ $ $ 1 $ $ $ 2 $ $ $ 3 $ $ $ 4 $ $ $ 5 $ $ $ Choose the correct graph of future value as a function of time and rate. Note: blue line is for 0%, orange line is for 4%, and grey line is for 25%. The correct graph is 7000 FV as Function of Time and Rate 6000 5000 4000 Future Value (5) A. 3000- 2000- 1000 Year 7000 FV as Function of Time and Rate 6000- 5000 4000 Future Value (S) B. 3000 2000 1000 7000 FV as Function of Time and Rate 6000 5000- 4000 C. Future Value S 3000- 2000 1000 Year 7000 FV as Function of Time and Rate 6000 5000 4000 Future Value (5) D. 3000- 2000 1000 c. Find the PV of $1,000 due in 6 years if the discount rate is 8%. Round your answer to the nearest cent. $ d. A security has a cost of $1,000 and will return $3,000 after 6 years. What rate of return does the security provide? Round your answer to two decimal places. % take for the population to e. Suppose California's population is 35.2 million people, and its population is expected to grow by 3% annually. How long will double? Round your answer to the nearest whole number. years f. Find the PV of an ordinary annuity that pays $1,000 each of the next 6 years if the interest rate is 10%. Then find the FV of that same annuity. Round your answers to the nearest cent. PV of ordinary annuity: $ FV of ordinary annuity: $ g. How will the PV and FV of the annuity in part f change if it is an annuity due rather than an ordinary annuity? Round your answers to the nearest cent. PV of annuity due: $ FV of annuity due: $ h. What will the FV and the PV for parts a and c be if the interest rate is 8% with semiannual compounding rather than 8% with annual compounding? Round your answers to the nearest cent. FV with semiannual compounding: $ PV with semiannual compounding: $ i. Find the annual payments for an ordinary annuity and an annuity due for 12 years with a PV of $1,000 and an interest rate of 6%. Round your answers to the nearest cent. Annual payment for ordinary annuity: $ Annual payment for annuity due: $ j. Find the PV and the FV of an investment that makes the following end-of-year payments. The interest rate is 6%. Year Payment $100 1 2 $200 $500 3 Round your answers to the nearest cent. PV of investment: $ FV of investment: $ k. Five banks offer nominal rates of 4% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. Assume 365 days in a year. 1. What effective annual rate does each bank pay? If you deposit $4,500 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? Round your answers to two decimal places. B D E EAR % % % % % FV after 1 year $ $ $ $ $ FV after 2 years $ $ $ $ $ 2. If the TVM is the only consideration, what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A? Round your answers to two decimal places. B D Nominal rate % % % % 3. Suppose you don't have the $4,500 but need it at the end of 1 year. You plan to make a series of deposits - annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E with payments beginning today. How large must the payments be to each bank? Round your answers to the nearest cent. B D E Payment $ $ $ 4. Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks? It is more likely that an investor would prefer the bank that compounded frequently. I. Suppose you borrow $14,000. The interest rate is 6%, and it requires 4 equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances. Round your answers to the nearest cent. If your answer is zero, enter "O". Beginning Balance Repayment of Principal Ending Balance Year Payment Interest 1 $ $ $ $ $ 2 $ $ $ $ $ 3 $ $ $ $ $ 4 $ $ $ $ Choose the correct graph that shows how the payments are divided between interest and principal repayment over time. The correct graph is Breakdown of payments Breakdown of payments 6000 6000- 5000 5000 4000 4000- Dollar Values 3000 Dollar Values 3000 A. B. 2000- 2000 LII 1000 1000 3 2 3 Year Year Repayment of Principal ($) Interest ($) Repayment of Principal ($) Interest ($) Breakdown of payments Breakdown of payments 6000- 6000- 5000 5000 4000- 4000+ Dollar Values 3000 Dollar Values 3000 C. D. 2000- 2000+ 1000 1000 1 2 3 1 3 Year Year Repayment of Principal ($) Interest ($) Repayment of Principal ($) Interest ($) Check My Work Reset
