andytrader

An investor who requires an annual return of 12% has the choice of receiving one of the following:

• 10 annual payments of $1,225.00 to begin at the end of one year.
• 10 annual payments of $1,097.96 beginning immediately.

Which option has the highest present value (PV) and approximately how much greater is it than the other option?

A) Option A's PV is $42 greater than option B's.

B) Option B's PV is $27 greater than option A's.

C) Option B's PV is $114 greater than option A's.

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Option A: N = 10, PMT = -$1,225, I = 12%, FV = 0, Compute PV = $6,921.52.
Option B: N = 9, PMT = -$1,097.96, I = 12%, FV = 0, Compute PV → $5,850.51 + 1,097.96 = 6,948.17 or put calculator in Begin mode N = 10, PMT = $1,097.96, I = 12%, FV = 0, Compute PV → $6,948.17. Difference between the 2 options = $6,921.52 − $6,948.17 = -$26.65.
Option B's PV is approximately $27 higher than option A's PV.

andytrader

A recent ad for a Roth IRA includes the statement that if a person invests $500 at the beginning of each month for 35 years, they could have $1,000,000 for retirement. Assuming monthly compounding, what annual interest rate is implied in this statement?

A) 7.625%.

B) 7.411%.

C) 6.988%.

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Solve for an annuity due with a future value of $1,000,000, a number of periods equal to (35 × 12) = 420, payments = -500, and present value = 0. Solve for i. i = 0.61761 × 12 = 7.411% stated annually. Don’t forget to set your calculator for payments at the beginning of the periods. If you don’t, you’ll get 7.437%.

andytrader

Which of the following statements about compounding and interest rates is least accurate?

A) All else equal, the longer the term of a loan, the lower will be the total interest you pay.

B) Present values and discount rates move in opposite directions.

C) On monthly compounded loans, the effective annual rate (EAR) will exceed the annual percentage rate (APR).

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Since the proportion of each payment going toward the principal decreases as the original loan maturity increases, the total dollars interest paid over the life of the loan also increases.

andytrader

Elise Corrs, hedge fund manager and avid downhill skier, was recently granted permission to take a 4 month sabbatical. During the sabbatical, (scheduled to start in 11 months), Corrs will ski at approximately 12 resorts located in the Austrian, Italian, and Swiss Alps. Corrs estimates that she will need $6,000 at the beginning of each month for expenses that month. (She has already financed her initial travel and equipment costs.) Her financial planner estimates that she will earn an annual rate of 8.5% during her savings period and an annual rate of return during her sabbatical of 9.5%. How much does she need to put in her savings account at the end of each month for the next 11 months to ensure the cash flow she needs over her sabbatical? Each month, Corrs should save approximately:

A) $2,065.

B) $2,080.

C) $2,070.

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This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we will use future value formulas to determine how much she needs to save each month.
Step 1:  Calculate present value of amount required during the sabbatical
Using a financial calculator: Set to BEGIN Mode, then N = 4; I/Y = 9.5 / 12 = 0.79167; PMT = 6,000; FV = 0; CPT → PV = -23,719.
Step 2:  Calculate amount to save each month
Using a financial calculator: Make sure it is set to END mode, then N = 11; I/Y = 8.5 / 12.0 = 0.70833; PV = 0; FV = 23,719; CPT → PMT= -2,081, or approximately $2,080.

andytrader

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:

A) $1,468; $1,702.

B) $1,650; $1,468.

C) $1,650; $1,702.

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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

andytrader

How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%?

A) $234,422.

B) $274,422.

C) $272,977.

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This is an annuity due so set your calculator to the BGN mode. N = 15; I/Y = 14.5; PMT = –40,000; FV = 0; CPT → PV = 274,422.50. Switch back to END mode.

andytrader

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?

A) $483.58.

B) $416.67.

C) $480.57.

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N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58.

andytrader

The First State Bank is willing to lend $100,000 for 4 years at a 12% rate of interest, with the loan to be repaid in equal semi-annual payments. Given the payments are to be made at the end of each 6-month period, how much will each loan payment be?

A) $25,450.

B) $32,925.

C) $16,104.

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N = 4 × 2 = 8; I/Y = 12/2 = 6; PV = -100,000; FV = 0; CPT → PMT = 16,103.59.

andytrader

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?

A) Investment B offers a $36.92 greater return.

B) Investment A offers a $122.18 greater return.

C) Investment A offers a $53.18 greater return.

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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.

andytrader

Steve Hall wants to give his son a new car for his graduation. If the cost of the car is $15,000 and Hall finances 80% of the value of the car for 36 months at 8% annual interest, his monthly payments will be:

A) $376.

B) $413.

C) $289.

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PV = 0.8 × 15,000 = -12,000; N = 36; I = 8/12 = 0.667; CPT → PMT = 376.