Flashcards in Module 4 Deck (19)

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1

## Chris received $13,000 from an inheritance, and he wants to invest it for the next 11 years. If he can earn 7.5% annually after tax, how much will his account be worth at the end of 11 years?

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The account is worth $28,803, with keystrokes on the HP 10bII/HP 10bII+ as follows:

13,000 PV

11 N

7.5 I/YR

Solve for FV = –28,802.9160 or $28,803

2

## Hector has been investing $2,000 at the end of each year for the past 18 years in a growth mutual fund. How much is the fund worth now assuming he has earned 10% compounded annually on his investment?

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The fund is worth $91,198, with keystrokes on the HP 10bII/HP 10bII+ as follows:

END mode

2,000 +/–PMT (Note: This is a cash outflow from the client; therefore, enter it as a negative amount.)

10 I/YR

18 N

Solve for FV = 91,198.3463, or $91,198

3

###
The fund is worth $91,198, with keystrokes on the HP 10bII/HP 10bII+ as follows:

END mode

2,000 +/–PMT (Note: This is a cash outflow from the client; therefore, enter it as a negative amount.)

10 I/YR

18 N

Solve for FV = 91,198.3463, or $91,198

4

## Peggy needs a total of $100,000 in 10 years to pay for four years of college for her granddaughter. If she can earn 7.5% annually after tax on her growth mutual fund set aside for this purpose, what single amount does Peggy need to invest today?

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Peggy needs to invest $48,519, with keystrokes on the HP 10bII/HP 10bII+ as follows:

100,000 FV

10 N

7.5 I/YR

Solve for PV = −48,519.3928, or $48,519 (Note: The HP 10bII/ HP 10bII+ calculator will return a negative number in this case. The negative sign displayed before the PV amount indicates that this investment is a cash outflow to Peggy.)

5

## Hannah invests $1,000 today with the hope that in five years her investment will be worth $1,500. The investment will compound semiannually. At the end of five years, what will be Hannah’s I/YR?

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The I/YR is 8.28%, with keystrokes on the HP 10bII/HP 10bII+ as follows:

1,000 +/− PV

1,500 FV

5 × 2 = 10 N

Solve for I/YR = 4.1380 × 2 = 8.2760, or 8.28%

6

##
Adam purchases a new car and finances $21,000 with a 5.9% loan over

three years. Assuming each payment is due on the first of each month, what is the amount of Adam’s monthly car payment?

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Adam’s car payment is $637.91, with keystrokes on the HP 10bII/HP 10bII+ as follows:

END mode

21,000 PV

5.9 ÷ 12 = 0.4917 I/YR

3 × 12 = 36 N

Solve for PMT = −637.9096, or $637.91 (Note: Because the PMT is a cash outflow for Adam, it is displayed as a negative number.)

NOTE: Loan amortizations (e.g., mortgages, auto loans) are calculated using END mode because the interest on the principal balance is accruing from payment to payment on the balance of the debt.

7

## Jack is buying a new car for $30,000 with a down payment of $2,000, and he is financing the balance of $28,000 with a five-year, 3.25% loan. What is Jack’s monthly payment, and how much interest will he pay over the life of the loan?

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Answer:

Make sure the calculator is in the END mode,

1 P/YR

28,000, PV

3.25 ÷ 12 = 0.2708,

I/YR 5 × 12 = 60, N

Solve for PMT = −506.2401, or $506.24

1, INPUT, 60

SHIFT, AMORT

= −28,000.0023 principal paid

= −2,374.4037 interest paid

= −0.0023 remaining balance (off by 0.0023 due to rounding)

8

###
Answer:

Make sure the calculator is in the END mode,

1 P/YR

28,000, PV

3.25 ÷ 12 = 0.2708,

I/YR 5 × 12 = 60, N

Solve for PMT = −506.2401, or $506.24

1, INPUT, 60

SHIFT, AMORT

= −28,000.0023 principal paid

= −2,374.4037 interest paid

= −0.0023 remaining balance (off by 0.0023 due to rounding)

9

##
(1) Jeremiah secures a $400,000 mortgage with a 15-year repayment term and an annual interest rate of 5.25%. Calculate the monthly payment on this loan.

(2) Continuing with the facts and inputs of the previous question, calculate the balance of Jeremiah’s mortgage at the end of 1 year (12 payments).

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(1) $3,215.51

(2) $381,984.47

10

## What would the inflation-adjusted interest rate be with a 7% rate of return and a 3% inflation rate?

###
1.03, INPUT

1.07, SHIFT, % CHG

3.88%

11

## Cheryl wants to receive the equivalent of $30,000 in today’s dollars at the beginning of each year for the next seven years. She assumes that inflation will average 4% over the long run and that she can earn a 9% compound annual after-tax return on investments. What lump sum does Cheryl need to invest today to achieve her goal?

### $183,211.73

12

## A client wants to save $125,000 to achieve a future goal. He has $26,000 to invest currently and can invest $10,000 at the end of each year toward his goal. If the investment vehicle selected earns 10% annually, how many years will it take to achieve his goal?

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END mode,

1 P/YR.

10, I/YR

26,000, +/−, PV

10,000, +/−, PMT

125,000, FV

Solve for N = 6.0835, or 6.08

13

## What is the average compound rate of return that has been earned from investing in an antique chair that was purchased six years ago for $1,000, was repaired at the end of the second year at a cost of $450, and has just sold for $2,850?

###
END mode, 1 P/YR

1,000, +/−, CFj

0, CFj

450, +/−, CFj

0, CFj

0, CFj

0, CFj

2,850, CFj

SHIFT, IRR/YR = 13.2502, or 13.25%

14

## A three-year investment in a mutual fund pays the following quarterly distributions: four distributions at $500, four at $570, and four at $600? These distributions are not reinvested back into the fund. The initial investment into the fund was $120,000, and the final value of the mutual fund account at the time of the last quarterly distribution was $165,000. What is the IRR earned?

###
END mode, 1 P/YR

120,000, +/−, CFj

500, CFj

4, SHIFT, N

570, CFj

4, SHIFT, Nj

600, CFj

3, SHIFT, Nj

165,600, CFj

SHIFT, IRR/YR = 3.0894 × 4 = 12.3577, or 12.36%

The IRR is 12.36%.

15

##
A real estate property being offered for $500,000 is expected to have cash flows of $30,000, $35,000, and $40,000 over each year in the following three-year period, respectively. At the end of three years, it is expected to have a value of $575,000. (Note that the last cash flow will be $40,000 + $575,000 = $615,000.)

If an investor has a required rate of return of 10%, what is the PV and NPV of the property?

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$518,256.95

END mode, 1 P/YR

0, CFj

30,000, CFj

35,000, CFj

615,000, CFj

10, I/YR

SHIFT, NPV = 518,256.9497, or $518,256.95

The PV (the price) that will allow a 10% return on the investment is $518,256.95. In other words, if the investor paid this amount and received the assumed cash flows, they would achieve a 10% return.

When the amount of the initial investment is subtracted from the PV, the result is referred to as the NPV.

$518,257 PV

$500,000 Initial investment

$ 18,257 NPV

16

##
What is the PV of an investment that would provide the following inflows, assuming that the client’s opportunity cost is 12%?

End of year 1 : $1,200

End of year 2 : $1,500

End of year 3 : $1,800

End of year 4 : $2,200

### $4,946.56

17

##
What is the PV of an investment that would provide the following inflows, assuming that the client’s opportunity cost is 12%?

End of year 1 : $1,200

End of year 2 : $1,500

End of year 3 : $1,800

End of year 4 : $2,200

### $4,946.56

18

## Glenda is considering the purchase of some rental property. The owner is asking $725,000, and the apartment units are expected to generate cash flows of $50,000, $55,000, $60,000, and $65,000 over the next four years. The property is expected to be worth $850,000 at the end of four years. What is the maximum amount that Glenda should pay for the property (its intrinsic value) if her required rate of return is 9%?

### $786,704.04

19