Sample

A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:

• a periodic interest rate of 0.667%.
• a stated rate of 0.830%.
• an effective annual rate of 8.00%.

Answer explanation

Periodic rate = 8.0 / 12 = 0.667. Stated rate is 8.0% and effective rate is 8.30%. (Study Session 1, Module 1.1, LOS 1.c)

A stated interest rate of 9% compounded quarterly results in an effective annual rate closest to:

• 0.093
• 0.094
• 0.092

Answer explanation

Quarterly rate = 0.09 / 4 = 0.0225. Effective annual rate = (1 + 0.0225)4 – 1 = 0.09308, or 9.308%.(Study Session 1, Module 1.1, LOS 1.c)

Peter Wallace wants to deposit $10,000 in a bank certificate of deposit (CD). Wallace is considering the following banks: Bank A offers 5.85% annual interest compounded annually. Bank B offers 5.75% annual interest rate compounded monthly. Bank C offers 5.70% annual interest compounded daily. Which bank offers the highest effective interest rate and how much?

• Bank B, 5.90%.
• Bank C, 5.87%.
• Bank A, 5.85%.

Answer explanation

Effective interest rates: Bank A = 5.85 (already annual compounding) Bank B, nominal = 5.75; C/Y = 12; effective = 5.90 Bank C, nominal = 5.70, C/Y = 365; effective = 5.87 Hence Bank B has the highest effective interest rate. (Study Session 1, Module 1.1, LOS 1.c)

Nikki Ali and Donald Ankard borrowed $15,000 to help finance their wedding and reception. The annual payment loan carries a term of seven years and an 11% interest rate. Respectively, the amount of the first payment that is interest and the amount of the second payment that is principal are approximately:

• $1,468; $1,702
• $1,650; $1,468
• $1,650; $1,702

Answer explanation

Step 1: Calculate the annual payment. Using a financial calculator (remember to clear your registers): PV = 15,000; FV = 0; I/Y = 11; N = 7; PMT = $3,183 Step 2: Calculate the portion of the first payment that is interest. Interest1 = Principal × Interest rate = (15,000 × 0.11) = 1,650 Step 3: Calculate the portion of the second payment that is principal. Principal1 = Payment – Interest1 = 3,183 – 1,650 = 1,533 (interest calculation is from Step 2) Interest2 = Principal remaining × Interest rate = [(15,000 – 1.533) × 0.11] = 1,481 Principal2 = Payment – Interest1 = 3,183 – 1,481 = 1,702 (Study Session 1, Module 1.3, LOS 1.f)

Fifty years ago, an investor bought a share of stock for $10. If the stock has experienced 2% compound annual growth over the period, its price today is closest to:

• $39
• $51
• $27

Answer explanation

10(1.02)50 = $26.91 Alternatively, N = 50; I/Y = 2; PV = –10; PMT = 0; CPT → FV = $26.91 (Study Session 1, Module 1.2, LOS 1.e)

Sarah Parker is buying a new $25,000 car. Her trade-in is worth $5,000 so she needs to borrow $20,000. The loan will be paid in 48 monthly installments and the annual interest rate on the loan is 7.5%. If the first payment is due at the end of the first month, what is Sarah's monthly car payment?

• $483.58
• $480.57
• $416.67

Answer explanation

N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58 (Study Session 1, Module 1.3, LOS 1.f)

Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today?

• $1,080,000
• $855,947.87
• $924,423.7

Answer explanation

First put your calculator in the BGN. N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70. Alternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1 + I/Y. You get the annuity due answer and you don't run the risk of forgetting to reset your calculator back to the end of the period setting. OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70. (Study Session 1, Module 1.2, LOS 1.e)

An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?

• $1,468
• $1,889
• $1,776

Answer explanation

The present value of the loan is $200,000 repayable over 30 × 12 = 360 months. The rate of interest per month is 8% / 12 = 0.67%. Using the calculator: PV = 200,000; FV = 0; N = 360; I/Y = 8 / 12 = 0.6667; CPT → PMT = $1,467.53. (Study Session 1, Module 1.3, LOS 1.f)

An investor has the choice of two investments. Investment A offers interest at 7.25% compounded quarterly. Investment B offers interest at the annual rate of 7.40%. Which investment offers the higher dollar return on an investment of $50,000 for two years, and by how much?

• Investment A offers a $122.18 greater return
• Investment B offers a $36.92 greater return
• Investment A offers a $53.18 greater return

Answer explanation

Investment A: I = 7.25 / 4; N = 2 × 4 = 8; PV = $50,000; PMT = 0; CPT → FV = $57,726.98 Investment B: I = 7.40; N = 2; PV = $50,000; PMT = 0; CPT → FV = $57,673.80 Difference = investment A offers a $53.18 greater dollar return. (Study Session 1, Module 1.3, LOS 1.f)

Paul Kohler inherits $50,000 and deposits it immediately in a bank account that pays 6% interest. No other deposits or withdrawals are made. In two years, what will be the account balance assuming monthly compounding?

• $50,500
• $53,100
• $56,400

Answer explanation

To compound monthly, remember to divide the interest rate by 12 (6%/12 = 0.50%) and the number of periods will be 2 years times 12 months (2 × 12 = 24 periods). The value after 24 periods is $50,000 × 1.00524 = $56,357.99. The problem can also be solved using the time value of money functions: N = 24; I/Y = 0.5; PMT = 0; PV = 50,000; CPT FV = $56,357.99. (Study Session 1, Module 1.1, LOS 1.d)