Question 1

You just won $50,000 and deposited your winnings into an account that pays 5.5 percent interest,compounded annually.How long will you have to wait until your winnings are worth $100,000?

Accepted Answer

$100,000 = $50,000 × (1 + 0.055)^t; t = 12.95 years

Question 2

When you were born,your parents opened an investment account in your name and deposited $500 into the account.The account has earned an average annual rate of return of 4.8 percent.Today,the account is valued at $36,911.22.How old are you?

Accepted Answer

$36,911.22 = $500 × (1 + 0.048)^t; t = 91.75 years

Question 3

Precision Engineering invested $110,000 at 6.5 percent interest,compounded annually for 4 years.How much interest on interest did the company earn over this period of time?

Accepted Answer

Interest on interest = $110,000 × (1 + 0.065)⁴ - [$110,000 + ($110,000 × 0.065 × 4)] = $2,911.30

Question 4

Which one of the following is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent.

Accepted Answer

The correct formula for present value is PV = FV / (1+r)^n, where FV = future value, r = discount rate, and n = number of years. Plugging in the values given in the question, we get PV = $600 / (1+0.07)^6 = $379.08. Option D is the only choice that correctly uses this formula.

Question 5

Twelve years ago,you deposited $3,400 into an account.Seven years ago,you added an additional $1,000 to this account.You earned 8 percent,compounded annually,for the first 5 years and 5.5 percent,compounded annually,for the last 7 years.How much money do you have in your account today?

Accepted Answer

Future value = {[$3,400 × (1 + 0.08)⁵] + $1,000} × (1 + 0.055)⁷ = $8,721.97

Question 6

Your grandparents just gave you a gift of $15,000.You are investing this money for 12 years at 6 percent simple interest.How much money will you have at the end of the 12 years?

Accepted Answer

Future value = $15,000 + ($15,000 × 0.06 × 12) = $25,800

Question 7

Centre Bank pays 2.5 percent interest,compounded annually,on its savings accounts.Country Bank pays 2.5 percent simple interest on its savings accounts.You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today.The amount you must deposit today:

Accepted Answer

Simple interest results in less interest accumulation over time compared to compound interest, so you need to deposit more initially with Country Bank to reach the same future amount.

Question 8

Which one of the following is a correct statement,all else held constant?

Accepted Answer

The answer of Which one of the following is a...

Question 9

Angela has just received an insurance settlement of $35,000.She wants to save this money until her daughter goes to college.If she can earn an average of 5.5 percent,compounded annually,how much will she have saved when her daughter enters college 10 years from now?

Accepted Answer

Future value = $35,000 × (1 + 0.055)¹⁰ = $59,785.06

Question 10

The relationship between the present value and the time period is best described as:

Accepted Answer

The relationship between the present value and the time period is inverse. This means that as the time period increases, the present value decreases. Similarly, as the time period decreases, the present value increases. This relationship is described by the time value of money concept, which suggests that money is worth more in the present than it is in the future due to factors such as inflation and opportunity cost.

Question 11

Jim just deposited $13,000 into his account at Traditions Bank.The bank will pay 1.3 percent interest,compounded annually,on this account.How much interest on interest will he earn over the next 15 years?

Accepted Answer

Interest on interest = $13,000 × (1 + 0.013)¹⁵ - [$13,000 + ($13,000 × 0.013 × 15)] = $244.20

Question 12

Your parents spent $6,200 to buy 500 shares of stock in a new company 13 years ago.The stock has appreciated 9 percent per year on average.What is the current value of those 500 shares?

Accepted Answer

Future value = $6,200 × (1 + 0.09)¹³ = $19,007.99

Question 13

Ben invested $5,000 twenty years ago with an insurance company that has paid him 5 percent simple interest on his funds.Charles invested $5,000 twenty years ago in a fund that has paid him 5 percent interest,compounded annually.How much more interest has Charles earned than Ben over the past 20 years?

Accepted Answer

Interest on interest = $5,000 × (1 + 0.05)²⁰ - [$5,000 + ($5,000 × 0.05 × 20)] = $3,266.49

Question 14

Travis invests $10,000 today into a retirement account.He expects to earn 8 percent,compounded annually,on his money for the next 26 years.After that,he wants to be more conservative,so only expects to earn 5 percent,compounded annually.How much money will he have in his account when he retires 38 years from now,assuming this is the only deposit he makes into the account?

Accepted Answer

Future value = $10,000 × (1 + 0.08)²⁶ × (1 + 0.05)^{(38 - 26)} = $132,827.88

Question 15

Today,you deposit $2,400 in a bank account that pays 4 percent simple interest.How much interest will you earn over the next 5 years?

Accepted Answer

Interest = $2,400 × 0.04 × 5 = $480

Question 16

Eric has $4,800 that he wants to invest for 4 years.He can invest this amount at his credit union and earn 4 percent simple interest.Or,he can open an account at Compass Bank and earn 3.65 percent interest,compounded annually.If he decides to invest at Copmpass Bank for 3 years,he will:

Accepted Answer

Credit union future value = $4,800 + ($4,800 × 0.04 × 4) = $5,568Compass Bank future value = $4,800 × (1 + 0.0365)⁴ = $5,540.11Difference = $5,568 - $5,540.11 = $27.89

Question 17

Today,Courtney wants to invest less than $5,000 with the goal of receiving $5,000 back some time in the future.Which one of the following statements is correct?

Accepted Answer

The answer of Today,Courtney wants to invest less than $5,000...

Question 18

What is the future value of $4,900 invested for 8 years at 7 percent compounded annually?

Accepted Answer

Future value = $4,900 × (1.07)⁸ = $8,419.11

Question 19

The present value of a lump sum future amount:

Accepted Answer

The answer of The present value of a lump sum...

Question 20

You want to invest an amount of money today and receive back twice that amount in the future.You expect to earn 6 percent interest.Approximately how long must you wait for your investment to double in value?

Accepted Answer

Approximate time period = 72/6 = 12 years

Quiz 4: Introduction to Valuation: The Time Value of Money