Time Value of Money

What is the future value of $1,000 invested today at an annual interest rate of 5% for 3 years?

• $1,050

• $1,150

• $1,157.63

• $1,200

Answer explanation

To find the future value, use the formula FV = P(1 + r)^n. Here, P = 1000, r = 0.05, and n = 3. Thus, FV = 1000(1 + 0.05)^3 = 1000(1.157625) = $1,157.63, which is the correct answer.

Scarlett and Maya are planning a trip to a dream destination in 5 years. They need $10,000 for the trip and can invest at an annual interest rate of 6%. How much should they invest today to make their dream come true?

• $7,472.58

• $7,913.48

• $8,375.29

• $9,000.00

Answer explanation

To find out how much to invest today, use the formula for present value: PV = FV / (1 + r)^n. Here, FV = $10,000, r = 0.06, and n = 5. This gives PV = 10000 / (1 + 0.06)^5 = $7,472.58.

Which of the following best describes an ordinary annuity?

• Payments are made at the beginning of each period.

• Payments are made at the end of each period.

• Payments are made semi-annually.

• Payments are made continuously over time.

Answer explanation

An ordinary annuity is defined as a series of payments made at the end of each period. This distinguishes it from an annuity due, where payments are made at the beginning of each period.

Kai and Nora decide to start a fun savings challenge! They each invest $5,000 at the beginning of every year for 10 years in an account that earns 8% interest. What type of annuity are they using?

• Ordinary annuity

• Annuity due

• Perpetuity

• Deferred annuity

Answer explanation

Kai and Nora are making their investments at the beginning of each year, which characterizes an annuity due. In contrast, an ordinary annuity involves payments made at the end of each period.

What is the present value of an annuity that pays $500 at the end of each year for 8 years, assuming a discount rate of 6%?

• $3,521.30

• $3,676.42

• $3,104.90

• $2,458.66

Answer explanation

To find the present value of the annuity, use the formula: PV = Pmt × [(1 - (1 + r)^-n) / r]. Here, Pmt = $500, r = 0.06, and n = 8. This calculates to approximately $3,104.90, confirming the correct choice.

Which of the following statements is true about the time value of money?

• A) Money received in the future is worth more than money received today.

• B) Money received today is worth more because it can earn interest.

• C) The time value of money only applies to large sums of money.

• D) Money has the same value regardless of when it is received.

Answer explanation

B is correct because money received today can be invested to earn interest, making it more valuable than the same amount received in the future. This concept is fundamental to the time value of money.

What happens to the present value of a future cash flow as the discount rate increases?

• A) It increases.

• B) It decreases.

• C) It stays the same.

• D) It depends on the time period.

Answer explanation

As the discount rate increases, the present value of a future cash flow decreases. This is because higher discount rates reduce the value of future cash flows, making them worth less in today's terms. Thus, the correct answer is B.

You are purchasing a vehicle for $45,000. After making a 10% down payment, you will finance the remaining balance. The loan will be repaid over 5 years at a nominal annual interest rate of 6%, with monthly payments (end of month). What will be your monthly payment?

• A) $658.12

• B) $753.89

• C) $710.25

• $782.98

Answer explanation

The down payment is $4,500 (10% of $45,000), leaving a loan amount of $40,500. Using the formula for monthly payments on an amortizing loan, the monthly payment calculates to $782.98.

Olivia and Benjamin are discussing their savings plans. Olivia says the future value of an annuity due is higher than the future value of an ordinary annuity, assuming the same interest rate and time period. Why is Olivia correct?

• Because payments are made at the end of each period.

• Because payments are made at the beginning of each period, earning interest longer.

• Because the interest rate is higher in an annuity due.

• Because annuities due have more periods than ordinary annuities.

Answer explanation

Olivia is correct because in an annuity due, payments are made at the beginning of each period, allowing them to earn interest for a longer time compared to an ordinary annuity, where payments are made at the end.

If the interest rate is zero, the present value of a sum to be received in the future is:

• Higher than the future sum.

• Lower than the future sum.

• Equal to the future sum.

• Dependent on the time period.

Answer explanation

If the interest rate is zero, there is no discounting effect on future sums. Therefore, the present value of a future sum is equal to that sum, making the correct answer 'Equal to the future sum.'