1. Midterm 1
Spring 2017

2. Problem 1
A stated annual interest rate of 18%, compounded 10 times per year, is equivalent to a stated annual interest rate of ________ if compounded 20 times per year
Answer:
−1= 1+ 𝑆𝐴𝑅 −1
= 1+ 𝑆𝐴𝑅
= 1+ 𝑆𝐴𝑅 20
= 𝑆𝐴𝑅 20
𝑆𝐴𝑅=

3. Problem 2
Oswald is receiving the money from a 50,000 loan later today. This loan has an 15% stated annual interest rate, compounded monthly, and a minimum monthly payment of 1% per month for the next year. The first payment for the loan will be one month from today. If he makes the minimum monthly payment each month, how much will his payment be two months from today? (Note: The minimum monthly payment is based off of the balance one month before the payment is made)
Answer:
Monthly rate= .15/12= .0125
Month
Previous Balance
Interest Accrued
Payment
New Balance 1
50,000
50,000*.0125= 625
50,000*.01=
500
50, =50,125 2
50,125
50,125*.0125=
626.56
50,125*.01=
501.25

4. Problem 3
Clarabelle has invested in a project with an internal rate of return of 5%. She makes a deposit today of $1,000 and receives a payment of $250 one year from today, $300 two years from today, $400 three years from today, and ____ four years from today.
Answer:
𝑁𝑃𝑉=− 𝑟 𝑟 𝑟 𝑥 1+𝑟 4
𝑁𝑃𝑉=− 𝑥 =0
− 𝑥 =0
𝑥=144.26∗ =175.35

5. If Sebastian invests in Y, he cannot invest in X
Problem 4
Sebastian is figuring out how to invest some money inherited from his aunt’s silver collection. If Investments X and Y are mutually exclusive, which of the following statements is true?
Answer:
Mutually exclusive investment decisions are investment decisions in which the acceptance of a project precludes (prevents) the acceptance of one or more alternative projects.
If Sebastian invests in Y, he cannot invest in X

6. Compound: FV=PV(1+r)^t
Problem 5
Roger is about to make a deposit in Doom National Bank. Roger does not know if he earns simple interest or compound interest. He makes a $10,000 deposit today and withdraws the money 5 years from today. If the annual interest rate if 20%, how much MORE interest does Roger earn with compound interest relative to simple interest?
Answer:
Simple: FV=PV(1+rT)
𝐹𝑉=10, ∗5 =20,000
Interest Accrued= 20,000-10,000=10,000
Compound: FV=PV(1+r)^t
𝐹𝑉=10, =24,883.2
Interest Accrued=24, ,000=14,883.2
Difference=14, ,000=4,883.2

7. PV of Loan Payments = Principle
Problem 6
Jessie buys a new house in Anaheim, California. The amount loaned for the mortgage is $600,000. The loan will be paid off with 400 equal monthly payments of $7,000, starting 24 months from today, and a balloon payment 425 months from today. The started annual interest rate is 12%, compounded monthly. How much must the balloon payment be in order to completely pay off the loan
Answer:
Monthly rate: .12/12=.01
PV of Loan Payments = Principle
600,000= 7, − ∗ 𝑋
600,000=546, 𝑋
53,593.71= 𝑋
𝑋=3,678,727

8. Problem 7a
Ichabod can purchase the Toad 3000 vacuum cleaner for $500. The machine lasts for six years, and has a $200 maintenance cost in three years. The relevant effective annual interest rate is 14%. What is the equivalent annual cost of this machine?
Answer:
PV of Costs = =634.99
634.99= 𝐸𝐴𝐶 −
634.99= ∗𝐸𝐴𝐶
𝐸𝐴𝐶=163.29

9. PV of Costs more when leasing, so Ichabod should BUY
Problem 7b
Ichabod could also lease the machine. If he leased the machine, he would have to pay $150 per year for each of the next six years. The first payment will be made today. Should Ichabod purchase or lease the machine?
Answer:
PV of Costs = − ∗1.14=664.96
>
PV of Costs more when leasing, so Ichabod should BUY