WEEK 3 LEARNING ACTIVITY ANSWERS

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University Of Arizona *

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Economics

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Jan 9, 2024

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LEARN QUESTION REVIEWING 10F 4 ANSWER INCORRECT James Suppose you win a lottery, and the lottery will pay you $1,000 per year, in perpetuity. Your siblings each offer to pay you the present value of lottery winnings in exchange for the future payments, but each uses a different discount rate to determine thelr offer price. ‘ THE CORRECT ANSWER Chris Your sibling James used an 8% discount rate. Your sibling Rosemary used a 12% discount rate. Your sibling Chris used a 5% discount rate. 'YOU WERE SURE AND INCORRECT Which sibling will give you the highest present value payment? Rosemary O IDON'TKNOW YET Which of the foll f cash flows has the I lue? . TR Which of the following streams of cash flows has the lowest present value Hiih Disooust Rate: Cash payment year I: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 15% O Medium Discount Rate: Cash payment year 1: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 8% ® YOU WERE SURE AND INCORRECT Low Discount Rate: Cash payment year 1: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 4%

QUESTION REVIEWING 30F 4 ANSWER Higher; lower When computing the future value of a single cash flow over a given time period, the _____ the interest rate, the ______ the future value (l) YOU WERE UNSURE AND CORRECT Higher; higher O Lower; higher O IDON'TKNOW YET QUESTION REVIEWING 4 OF 4 ANSWER CORRECT S 'YOU WERE UNSURE AND CORRECT In the equation to calculate the future value of a stream of cash flows, what does the subscript N The subscript refers to the number of compounding periods, where n is a n attached to FV refer to? unit of time such as a year FV, =CF x(1 +n)"' +CR x (1 +7)"? +...CF, \ The subscript n indicates multiplication. The subscript n indicates the discount rate. The subscript n refers to the present time. The subscript n indicates division. IDON'TKNOW YET 00000

The same as You have two cousins that each borrowed $100 from you. Cousin Jack has promised to pay you the $100 in 2 years, while cousin Kate has promised to pay you the $100 in 5 years. (Neither cousin is paying you interest!). THE CORRECT ANSWER L Less than The payment from Kate is worth the payment from Jack. YOU WERE SURE AND INCORRECT More than IDON'T KNOW YET O® 0O QUESTION ANSWER The n applied to (1 + r) indicates division. In the equation to calculate the future value of a single cash flow, what does the n as applied to the expression (1+r) mean? 'YOU WERE SURE AND CORRECT The n applied to (1 + r) indicates an exponent, and raises the expression (1 + 1) to the power of n FV, =PV 14+7)" n — 0 X T The n applied to (1 + r) indicates the discount rate. The n applied to (1 + r) indicates addition. The n applied to (1 + 1) refers to the present time YOOO ®0O

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. THE CORRECT ANSWER Which of the following single cash payments (received at the future time indicated) has the Esing P ¢ ) Short Time Period: highest present value? Cash payment: $6,000 Paid in: 4 years Discount rate: 8% @ YOU WERE UNSURE AND INCORRECT Long Time Period: Cash payment: $6,000 Paid in: 15 years Discount rate: 8% O Medium Time Period: Cash payment: $6,000 Paid in: 10 years Discount rate: 8% m IDON'TKNOW YET You will receive a payment of $5,000 six years from now. Your friend is willing to pay you $4,500 now in exchange for your future payment. Assuming a discount rate of 4% (compounded), which is worth more today, the payment of of $4,500? ix years or your friend’s payment today OO ®0O Both payments are equal. YOU WERE SURE AND CORRECT The friend’s payment of $4,500 is worth more today. The payment of $5,000 (in six years) is worth more today. I DON'T KNOW YET

Which of the following future single cash payments has the lowest present value? QUESTION REVIEWING 10F 2 You plan to deposit $500 per year into a savings account for 3 years. The savings account will earn 7% interest, compounded annually. Your best friend is also planning to deposit $500 per year into a savings account for 3 years. Your best friend's bank is offering a savings account that pays 12% interest, compounded annually. Who will have less money saved at the end of the 3 years? THE CORRECT ANSWER High Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 12% Medium Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 8% YOU WERE UNSURE AND INCORRECT Low Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 3% O I DON'TKNOW YET ANSWER INCORRECT ® YOU WERE SURE AND INCORRECT Your best friend will have less money saved THE CORRECT ANSWER You will have less money saved I DONTKNOW YET O You and your best friend will have the same amount of money saved

QUESTION REVIEWING 5 OF 6 ANSWER CORRE You plan to deposit $500 per year into a savings account for 4 years. The savings account will <D YOU WERE UNSURE AND CORRECT Lk Your best friend will have more money saved earn 7% interest, compounded annually. Your best friend is also planning to deposit S500 per year into a savings account for 4 years. O You will have more money saved Your best friend’s bank is offering a savings account that pays 12% interest, compounded annually. ; s : 3 2 You and your best friend will have the same amount of money saved O I DON'TKNOW YET Who will have more money saved at the end of the 4 years? 0.9 In the following problem, what decimal number do you use for r in order to solve the equation? YOU WERE UNSURE AND CORRECT Using the following equation, compute the future value of $500, at an interest rate of 9% compounded annually, in 5 years. 0.09 FV, =PV x(1+7)" 9 0.5 5 | DON'T KNOW YET YOU WERE SURE AND CORRECT In the equation to calculate the future value of a stream of cash flows, what do the subscripts 1, : E . - g . h The subscripts 1, 2, and n refer to the time period for the cash flow, in units 2, and n attached to the CFs refers to? FV, =CF, x(1 +7)" ! +CHh x(1 +1)"? +...CF, \ of time such as years. The subscripts 1, 2, and n refer to the multiplication of the interest rate. The subscripts 1, 2, and n refer to the discount rate. The subscripts 1, 2, and n refer to the present time. OO0 ® OO0OOeO0

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[T R o vy o i The subscript n indicates division. In the equation to calculate the present value of a single cash flow, what does the subscript n after FV refer to? 'YOU WERE SURE AND CORRECT PV FV. -n The subscript n indicates the time period is in the future at time n 0 = n X (1+7‘) The subscript n refers to the value at time zero, The subscript n indicates the discount rate. The subscript n indicates multiplication. IDON'TKNOW YET O000O ®0O Chris Suppose you win a lottery, and the lottery will pay you $1,000 per year, in perpetuity. Your siblings each offer to pay you the present value of lottery winnings in exchange for the future payments, but each uses a different discount rate to determine their offer price. YOU WERE SURE AND CORRECT Rosemary Your sibling James used an 8% discount rate. Your sibling Rosemary used a 12% discount rate. . Your sibling Chris used a 5% discount rate. James Which sibling will give you the lowest present value payment? IDON'TKNOW YET OO ®O

Which of the following streams of cash flows has the highest present value? Which of the following single cash flows has the highest future value, assuming compound interest? O @ O C) @ O O High Discount Rate: Cash payment year I: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 15% YOU WERE SURE AND CORRECT Low Discount Rate: Cash payment year I: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 4% Medium Discount Rate: Cash payment year I: $100 Cash payment year 2: $100 Cash payment year 3: $100 Discount rate: 8% Medium Time Period: $3,000 cash flow 4% interest 7years 'YOU WERE SURE AND CORRECT Long Time Period: $3,000 cash flow 4% interest 10 years Short Time Period: $3,000 cash flow 4% interest rate 4years IDON'TKNOW YET

QUESTION REVIEWING 2 OF 2 You and your friend each intend to save $2,000 for five years. Your friend finds a savings account that pays 3% interest (compounded). You find a saving account that pays 5% interest (compounded). The total amount you will have at the end of five years will be the amount your friend has. QUESITIVUN You have two cousins that each borrowed $100 from you. Cousin Jack has promised to pay you the $100 in 2 years, while cousin Kate has promised to pay you the $100 in 5 years. (Neither cousin is paying you interest!) The payment from Jack is worth the payment from Kate ANSWER G) YOU WERE UNSURE AND INCORRECT Less than O Equal to THE CORRECT ANSWER More than O IDON'TKNOW YET ANDVVEK O Less than @ 'YOU WERE SURE AND CORRECT More than O IDON'TKNOW YET

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YLoTIvIY RINo VYL Lower; lower When computing the present value of a single cash flow over a given time period, the _____ the interest rate, the the present value. O Higher; higher (D YOU WERE UNSURE AND CORRECT Lower; higher O IDON'TKNOW YET Shorter; higher When computing the future value of a single cash flow with a given interest rate, the the time period, the the future value. Longer, lower 'YOU WERE UNSURE AND CORRECT Longer; higher IDON'T KNOW YET Oe0O0

'YOU WERE UNSURE AND CORRECT Which of the following future single cash payments has the highest present value? A Low Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 3% O High Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 12% O Medium Discount Rate: Cash payment: $2,000 Paid in: 4 years Discount rate: 8% N inenerencwver <D YOU WERE UNSURE AND CORRECT Which of the following single cash payments (received at the time indicated) has the lowest : i Long Time Period: present value? Cash payment: $6.000 Paid in: 15 years Discount rate: 8% O Short Time Period: Cash payment: $6,000 Paid in: 4 years Discount rate: 8% O Medium Time Period: Cash payment: $6,000 Paid in: 10 years Discount rate: 8% O IDON'TKNOW YET

WEEK 3 LEARNING ACTIVITY ANSWERS

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