Present and Future Value

**Question 4**

In 1880, five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1994, the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest.

- How much was each granddaughter entitled to if the interest rate was 3%?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Future value – 2,906.99 Australian dollars

- How much was each entitled to if the interest rate was 6%?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Future value – 76,712.94 Australian dollars

Present and Future Value

**Question 7**

A factory costs $290,000. You forecast that it will produce cash inflows of $85,000 in year 1, $145,000 in year 2, and $230,000 in year 3. The discount rate is 10%.

- What is the value of the factory?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Value of the factory $ 76.783.80

- Is the factory a good investment?

Yes

No

Present and Future Value

**Question 8**

A famous quarterback just signed a $19.2 million contract providing $3.2 million a year for 6 years. A less famous receiver signed a $21.2 million 6-year contract providing $5 million now and $2.8 million a year for 6 years. The interest rate is 9%.

- What is the PV of the quarterback’s contract?

**Note: Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.**

Present value __________ million

- What is the PV of the receiver’s contract?

**Note: Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.**

Present value _____________ million

- Who is better paid?

- Quarterback
- Receiver

Present and Future Value

**Question 9**

- If you borrow $1,900 and agree to repay the loan in five equal annual payments at an interest rate of 12%, what will your payment be?

Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Amount of payment______________________

- What will your payment be if you make the first payment on the loan immediately instead of at the end of the first year?

Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Amount of payment______________________

Present and Future Value

**Question 10**

A couple will retire in 50 years; they plan to spend about $36,000 a year (in current dollars) in retirement, which should last about 25 years. They believe that they can earn a real interest rate of 8% on retirement savings.

- If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year.

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Annual savings ________________

- How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend $66,000 on their child’s college education?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Annual savings _________________

Present and Future Value

**Question 11**

A store will give you a 3.25% discount on the cost of your purchase if you pay cash today. Otherwise, you will be billed the full price with payment due in 1 month. What is the implicit borrowing rate being paid by customers who choose to defer payment for the month?

**Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.**

Effective annual rate ______ %

**Question 12**

- How much will $100 grow to if invested at a continuously compounded interest rate of 12.5% for 9 years?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Future value _______________

- How much will $100 grow to if invested at a continuously compounded interest rate of 9% for 12.5 years?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

Future value ______________

Present and Future Value

**Question 13**

In December 2020, a pound of lemons cost $1.48, while a pound of bananas cost $1.12. Three years earlier, the price of lemons was $1.27 a pound and that of bananas was $0.98.

- What was the annual compound rate of growth in the price of lemons?

**Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places. Negative answers should be indicated with a minus sign.**

- What was the annual compound rate of growth in the price of bananas?

**Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.**

- If the same rates of growth persist in the future, what will be the price of lemons in 2030?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

- What about the price of bananas?

**Note: Do not round intermediate calculations. Round your answer to 2 decimal places.**

- Compound annual growth rate of lemons _____ %
- Compound annual growth rate of bananas _____ %
- Price of lemons
- Price of bananas

Present and Future Value

**Question 14**

An engineer in 1950 was earning $6,400 a year. In 2020, she earned $84,000 a year. However, on average, prices in 2020 were higher than in 1950. What was her real income in 2020 in terms of constant 1950 dollars? Use the data in Table 5.8.

**Note: Round your answer to 2 decimal places.**

Real income in 2020 _____________

APA.