Rationale What don't we know Present Value (PV) or Future Value (FV) Problem Single Amount (1), or Multiple same payments Annuity (A) Choose FV1, FVA, PV1, or PVA, , and periods TVMF from the Chart Amount Calculation Answer 1 Your Grandmother deposited $5000 in the bank for you at 4 5 interest, compounding annually (e g , one time per year) How much will you have at the end of seven years We know a single amount that is going into the bank now (presently), but wedon't know what it will be in thefuture So wewant to know the Future Value of one dollar amount FV1,4 5 ,7 1 36086 $ 5,000 5000 1 36086 $ 6,804 30 2 Your company has borrowed $75000 and is expected to pay the borrowed amount plus 12 interest compounded annually at the end of six years How much is the payment at the end of the sixth year We know a single amount that is being borrowed now (presently), but wedon't know what is owed in thefuture So wewant to know the Future Value of one dollar amount $ 75,000 3 Your Dad deposited $9000 in the bank for you at 6 interest, compounding quarterly (e g , 4 times per year) How much will you have at the end of five years 4 To calculate the proceeds, add the amounts from the two present value calculations above B11 H14 $ 9,000 4 Smith company deposited $12000 per year for 5 years, into an account paying 7 interest, compounded annually What is the balance of the account at the end of the 5th year We know multiple payments that will be going into the bank now (presently) and annually, but we don't know the value in thefuture So we want to know the Future Value of multiple payments of the same amount (annuity) $ 12,000 5 Young Company issued $200,000, 8 year bonds and has agreed to make annual sinking fund deposits of $20000 The deposits are made at the end of each year to a fund paying 6 interest compounded annually What amount will be in the sinking fund at the end of the 8 years Don't be fooled by the $200,000 bond You aren't calculating that The company is setting aside money (the sinking fund) to eventually pay back this bond This is a series of payments (annuity) for which we want the value in thefuture $ 20,000 6 The Johnson Company is considering investing in an annuity contract that will return $12000 annually at the end of each year for 15 years What amount should the Savmore Johnson pay for this investment if it earns an 6 return We want $12000 every year (annuity) for 15 years (in the future) How much will it cost us in the present $ 12,000 7 What is the present value of $15000 due 7 years from now, discounted at 8 We know the future value What is the present value of thisone amount $ 15,000 8 What is the present value of $10000 due 10 years from now, discounted at 4 We know the future value What is the present value of thisone amount $ 10,000 9 The Venezia Company is considering an investment that will return a lump sum of $4000000 seven years from now What amount should Venezia Company pay for this investment to earn an 12 return We know the future value What is the present value of thisone amount $ 4,000,000 10 The LSL Company has decided to begin accumulating a fund for company expansion The company deposited $20000 in a fund on January 2, 2024 LSL will also deposit $4000 annually at the end of each year, starting in 2024 The fund pays interest at 6 compounded annually What is the balance of the fund at the end of 2029 (after the 2029 deposit) We know the single amountthat is being deposited today, but we don't yet know its value in the future We know the recurring (annuity) amount that we are depositing starting at the end of this year, and continuing for four years Including interest, we need the total in thefuture Add these two amounts $ 20,000 $ 4,000 11 Barrett Company issued 9 , 5 year, $900000 par value bonds that pay interest semiannually on October 1 and April 1 The bonds are dated April 1, 2024, and are issued on that date The discount rate of interest for such bonds on April 1, 2024, is 10 What cash proceeds did Barrett Company receive from issuance of the bonds Multi step approach We know the future amount how much should we pay now (in the present) 1 Calculate the cash interest payments that are promised Use the coupon rate or just the stated rate Note If interest payments are made semi annually, divide the rate by 2 For the next steps, you'll need to find the Time Value of Money Factor (TVMF) To find the TVMF, use the market or discount rate however, to find the (column), divide the rate by the number of payments per year To find the number of periods (row) multiply the years by the number of payments per year 2 Calculate thepresent value of these semi annual cash payments (annuity) We need the present value of the regular interest payments 3 Calculate the present value of thesingle amount (the face value , lump sum , the big number) Use the same percentage and number of periods that you used for the calculation above $ 900,000 4 To calculate the proceeds, add the amounts from the two present value calculations above 12 Bonus If Chris Kikuchi invests $2992 50 now, she will receive $10000 at the end of 14 years What annual rate of return will Chris earn on their investment We know the present value, we know the future value, we know the periods We don't know the TVMF We can find the rate by dividing the present value by the present value, and looking in the row of 14 periods and seeing which TVMF is equal in the Present Value of a single amount $ 10,000 $ 2,992 50 13 Bonus Cessa HJ purchased an investment for $9818 15 From this investment, Cessa will receive $1000 annually for the next 20 years starting one year from now What rate of interest will Cessa be earning on the investment We know the present value We know the regular payments (annuity) and we know the term We can find the rate by looking in the row of 20 periods and seeing which TVMF is equal to the Present Value divided by the payments (annuity) $ 1,000 $ 9,818 15 A brief example of Future Value usage Your Grandmother gives you $3,000 today and you decide to put it into a savings account with 3 earning, compounding once per year How much will you have at the end of 3 years Would you know which TVMF Table to use They are listed as Tables 1 4, but quite frankly, I forget which is which I'm more interested in if it's the Present Value of a single amount (PV1), Present Value of an Annuity (PVA), the Future Value of a single amount (FV1), or the Future Value of an Annuity (FVA)

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Rationale: What don't we know? Present Value (PV) or Future Value (FV) Problem? Single Amount (1), or Multiple same payments Annuity (A)? Choose: FV1, FVA,


	Rationale: What don't we know? Present Value (PV) or Future Value (FV) Problem? Single Amount (1), or Multiple same payments "Annuity" (A)?		Choose: FV1, FVA, PV1, or PVA,%, and periods.	TVMF from the Chart	Amount	Calculation	Answer
1	Your Grandmother deposited $5000 in the bank for you at 4.5% interest, compounding annually (e.g., one time per year). How much will you have at the end of seven years?	We know a single amount that is going into the bank now (presently), but wedon't know what it will be in thefuture. So wewant to know the Future Value of one dollar amount.	FV1,4.5%,7	1.36086	$ 5,000	= 5000 * 1.36086	$ 6,804.30
2	Your company has borrowed $75000 and is expected to pay the borrowed amount plus 12% interest compounded annually at the end of six years. How much is the payment at the end of the sixth year?	We know a single amount that is being borrowed now (presently), but wedon't know what is owed in thefuture. So wewant to know the Future Value of one dollar amount.			$ 75,000
3	Your Dad deposited $9000 in the bank for you at 6% interest, compounding quarterly (e.g., 4 times per year). How much will you have at the end of five years?	4. To calculate the proceeds, add the amounts from the two present value calculations above.B11:H14			$ 9,000
4	Smith company deposited $12000 per year for 5 years, into an account paying 7% interest, compounded annually. What is the balance of the account at the end of the 5th year?	We know multiple payments that will be going into the bank now (presently) and annually, but we don't know the value in thefuture. So we want to know the Future Value of multiple payments of the same amount (annuity).			$ 12,000
5	Young Company issued $200,000, 8-year bonds and has agreed to make annual sinking fund deposits of $20000. The deposits are made at the end of each year to a fund paying 6% interest compounded annually. What amount will be in the sinking fund at the end of the 8 years?	Don't be fooled by the $200,000 bond. You aren't calculating that. The company is setting aside money (the sinking fund) to eventually pay back this bond. This is a series of payments (annuity) for which we want the value in thefuture.			$ 20,000
6	The Johnson Company is considering investing in an annuity contract that will return $12000 annually at the end of each year for 15 years. What amount should the Savmore Johnson pay for this investment if it earns an 6% return?	We want $12000 every year (annuity) for 15 years (in the future). How much will it cost us in the present?			$ 12,000
7	What is the present value of $15000 due 7 years from now, discounted at 8%?	We know the future value. What is the present value of thisone amount?			$ 15,000
8	What is the present value of $10000 due 10 years from now, discounted at 4%?	We know the future value. What is the present value of thisone amount?			$ 10,000
9	The Venezia Company is considering an investment that will return a lump sum of $4000000 seven years from now. What amount should Venezia Company pay for this investment to earn an 12% return?	We know the future value. What is the present value of thisone amount?			$ 4,000,000
10	The LSL Company has decided to begin accumulating a fund for company expansion. The company deposited $20000 in a fund on January 2, 2024. LSL will also deposit $4000 annually at the end of each year, starting in 2024. The fund pays interest at 6% compounded annually. What is the balance of the fund at the end of 2029 (after the 2029 deposit)?	We know the single amountthat is being deposited today, but we don't yet know its value in the future. We know the recurring (annuity) amount that we are depositing starting at the end of this year, and continuing for four years. Including interest, we need the total in thefuture. Add these two amounts.			$ 20,000
					$ 4,000

11	Barrett Company issued 9%, 5-year, $900000 par value bonds that pay interest semiannually on October 1 and April 1. The bonds are dated April 1, 2024, and are issued on that date. The discount rate of interest for such bonds on April 1, 2024, is 10%. What cash proceeds did Barrett Company receive from issuance of the bonds?	Multi-step approach: We know the future amount - how much should we pay now (in the present)? 1. Calculate the cash interest payments that are promised. Use the "coupon" rate or just the stated rate.Note: If interest payments are made semi-annually, divide the rate by 2.
		For the next steps, you'll need to find the Time Value of Money Factor (TVMF). To find the TVMF, use the "market" or "discount" rate; however, to find the % (column), divide the % rate by the number of payments per year. To find the number of periods (row) multiply the years by the number of payments per year. 2. Calculate thepresent value of these semi-annual cash payments (annuity). We need the present value of the regular interest payments.
		3. Calculate the present value of thesingle amount (the "face value", "lump sum", the big number). Use the same percentage and number of periods that you used for the calculation above.			$ 900,000
		4. To calculate the proceeds, add the amounts from the two present value calculations above.
12	Bonus If Chris Kikuchi invests $2992.50 now, she will receive $10000 at the end of 14 years. What annual rate of return will Chris earn on their investment?	We know the present value, we know the future value, we know the periods. We don't know the TVMF. We can find the rate by dividing the present value by the present value, and looking in the row of 14 periods and seeing which TVMF is equal in the Present Value of a single amount.			$ 10,000		$ 2,992.50
13	Bonus Cessa HJ purchased an investment for $9818.15. From this investment, Cessa will receive $1000 annually for the next 20 years starting one year from now. What rate of interest will Cessa be earning on the investment?	We know the present value. We know the regular payments (annuity) and we know the term. We can find the rate by looking in the row of 20 periods and seeing which TVMF is equal to the Present Value divided by the payments (annuity).			$ 1,000		$ 9,818.15

A brief example of Future Value usage: "Your Grandmother gives you $3,000 today and you decide to put it into a savings account with 3% earning, compounding once per year. How much will you have at the end of 3 years? Would you know which TVMF Table to use? They are listed as Tables 1-4, but quite frankly, I forget which is which. I'm more interested in if it's the Present Value of a single amount (PV1), Present Value of an Annuity (PVA), the Future Value of a single amount (FV1), or the Future Value of an Annuity (FVA).