Finance Ch. 4

True or false: If you invest $1,000 and earn compound interest, the dollar amount of your annual interest payment will increase will increase each year.

True Interest earnings are added your investment each year so the next year's interest payment will be larger than this years.

Ten years ago, Alicia invested $9,000 at 5% interest. How much more money would she have today if she had invested the money at 6% instead of 5%? Interest is compounded annually.

$1,457.58

What is the value today of $2,500 to be received in 7 years if the discount rate is 3.5%?

$1,964.98

Louisa invested $12,000 in a business venture which returned $4,000, $6,000 and $8,000 over the past three years. Which of these amounts is (are) cash outflows to Louisa?

$12,000 investment

Five years ago, Lewis Equipment purchased equipment costing $212,000. Two years ago, the firm paid $32,000 for updates to that equipment. This year, the firm sold the equipment for $189,000. Which of these cash flows is (are) cash inflows to Lewis Equipment?

$189,000 sale price

A bank loaned money at 7% interest for five years to Stu. The loan will be repaid in one lump sum payment of $3,366.12. How much did Stu borrow?

$2,400

Susette invested $10,000 twenty years ago. Ten years ago, she invested an additional $5,000. Last year, she withdrew $8,000 to pay for a vacation. If you were to draw a time line of these events, which value(s) would be treated as a cash inflow(s) to Susette?

$8,000 cash withdrawal

You expect to receive a gift of $1,000 three years from today. What is the value of this gift today if the discount rates are 6%, 6.5% and 7% for the next three years, respectively?

$827.87

A project has these cash flows: -$2,000 two years ago, $800 one year ago, and $1,200 one year from now. Which is the correct formula for computing today's value of these cash flows given a 6% rate of interest?

=-$2,000 x (1+0.06)2 + $800 x (1+0.06) + $1,200/(1+0.06)

Which one of these statements is correct concering the relationship of PV, FV, i and N? Assume the interest rate is constant and positive.

All else held constant, the longer the period, the lower the present value

Which one of the following best illustrates simple interest?

Ann has a $1,000 savings account that will pay her $40 of interest each year for 5 years

What annual rate of return is earned on a $4,000 investment made in year 3 when it grows to $8,600 by the end of year 9? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Annual rate of return 13.61 ± 1% Explanation: FVN = PV × (1 + i)N FV9 = PV3 × (1 + i) (9 - 3) $8,600 = $4,000 × (1 + i)6 (1 + i)6 = $8,600 / $4,000 i = (2.15) (1 / 6) - 1 = 1.1361 - 1 = 0.1361 or 13.61%

Which one of these cash flows best illustrates a cash outflow?

Better Bakery purchased an oven for $28,600

You are scheduled to receive a $400 cash flow in one year, a $900 cash flow in two years, and pay a $700 payment in three years. Interest rates are 8 percent per year. What is the combined present value of these cash flows? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Combined present value of cash flows $ 586.29

Which of these is the definition of the compounding of interest?

Compounding is the process of earning interest both on the original investment and on the interest payments received earlier

Which one of these is the definition of the compounding of interest?

Compounding is the process of earning interest both on the original investment and on the interest payments received earlier

True or False: Several years ago, your grandmother invested $500 for you at 2.5% interest. Today, that investment is worth $1,864. When computing the number of years, the $1,864 should be used as the present value.

False $1,864 is the future value. The present value is $500

Consider a $5,800 deposit earning 8 percent interest per year for 8 years. What is the future value? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) How much total interest is earned on the original deposit? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Future Value 10,735.40 ± 0.1% Total Interest Earned 4,935.40 ± 0.1% Interest earned on the interest 1,223.40 ± 0.1% Explanation: The $5,800 investment will grow to a future value of $10,735.40 [= FV8 = $5,800 × (1 + 0.08)8], assuming compounded interest over the 8 years. The total interest earned is $4,935.40. The interest earned on the original investment is $464 per year for 8 years, or $3,712. The interest earned on the interest is the difference of $1,223.40 [= $4,935.40 − $3,712].

How is future value best defined?

Future value is the value of an investment after one or more periods

Solving which of the following problems illustrates discounting?

How much do you need to invest today at 7% interest to have $40,000 available for college expenses in 17 years? What is a $1,000 gift to be received next year worth today if the interest rate is 5%?

Which of these is the correct formula for computing the interest rate on an investment?

I(FVn/PV)1/n-1

Which one of these statements is correct concerning the relationship of I to PV, FV and N

If you increase the interest rate, all else held constant, the future value will increase

$100 represents the present value, as it is used in the present value formula, for which of these problems?

Janice invested $100 today at 9% interest for 10 years Russ' savings account increased in value from $100 five years ago to $111 today

Charity House has been promised a $25,000 donation five years from today. How much would that gift be worth next year? Assume an interest rate of 8%

PV= $25,000/(1+0.08)4

Which one of the following is the correct application of the present value formula for this problem: Maria expects to receive $5,000 from her grandmother upon her graduation in three years. What is the current value of this gift if the interest rate is 4%?

PV= $5,000/(1+0.04)8

You expect to receive a gift of $5,000 six years from today. Which formula provides the value of this gift two years from today if the discount is 9%?

PV= $5,000/(1+0.09)4

How long will it take $2,000 to reach $3,400 when it grows at 10 percent per year? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Period 5.56 correct years Explanation: FVN = PV × (1 + i)N $3,400 = $2,000 × (1 + 0.10)N (1.10)N = $3,400 / $2,000 (the thousands cancel) ln (1.10)N = ln 1.7 N × ln 1.10 = ln 1.7 N = ln 1.7 / ln 1.10 = 0.53063 / 0.09531 = 5.57 years = 5 years, 6.8 months

Compute the present value of $4,100 paid in two years using the following discount rates: 9 percent in the first year and 8 percent in the second year. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Present value $ 3,482.84

Compute the present value of $900 paid in three years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8 percent in the third year. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Present value $ 734.73

You invested $3,000 in the stock market one year ago. Today, the investment is valued at $3,450. What return did you earn? What return would you suffer next year for your investment to be valued at the original $3,000? (Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Return earned 15 ± 1% % Return earned -13.04 ± 1% % Explanation: FVN = PV × (1 + i)N $3,450 = $3,000 × (1 + i)1 (1 + i) = $3,450 / $3,000 i = 1.15 - 1 = 0.15 or 15.00% (first year return is positive) FVN = PV × (1 + i)N $3,000 = $3,450 × (1 + i)1 (1 + i) = $3,000 / $3,450 i = 0.8696 - 1 = -0.1304 or -13.04% (second year return is negative)

Which of these statements is (are) correct? Assume a constant, positive, annual rate of interest.

The longer the time period, the greater the future value of a stated sum The shorter the time period, the higher the present value of a stated future value

What is the value in year 4 of a $730 cash flow made in year 7 if interest rates are 10 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Value in year 4 $ 548.46 correct

Ten years ago, Hailey invested $3,900 and locked in an 8 percent annual interest rate for 30 years (ending 20 years from now). Aidan can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Hailey? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

5,833.42 ± 0.1% Explanation: First, determine how much Hailey will have 20 years from now: FV20 = PV -10 × (1 + i)30 FV20 = $3,900 × (1 + 0.08)30 = $3,900 × 10.0627 = $39,244.36 (Hailey's FV in 30 years) So, Aidan will have to deposit: PV = FV20 / (1 + i)N PV = $39,244.36 / (1 + 0.10)20 = $39,244.36 / 6.7275 = $5,833.42

Which formula computes the value in year 9 of a $10,000 investment in year 2 if the interest rate is 6%

FV= $10,000 x (1+0.06)7

Which formula illustrates the value of $100 invested for one year at 5% interest?

FV= $100 x (1+0.05)

How is the future value of $500 invested for one year at 6% annual interest computed?

FV= $500 x (1+0.06)1

Which formula moves a cash flow of $800 ahead six years in time at an interest rate of 5 percent?

FV= $800 x (1+0.05)6

A deposit of $820 earns interest rates of 8 percent in the first year and 11 percent in the second year. What would be the second year future value?

Future value $ 983.01 Explanation: The time line for this problem is: FV = PV × (1 + i) (1 + j) FV = $820 × (1 + 0.08) (1 + 0.11) = $820 × 1.08 × 1.11 = $983.02

Which one of these correctly defines the future value of a $1,000 investment?

Future value is the value of the investment at any date after the initial investment date

Today, both Marti and Neil invested $5,000. Marti's investment will return will return 4% while Neil's will return 8%. Both rates will be compounded. Which one of these statements is correct?

Neil's investment will increase in value faster than Marti's