1) Your brother-in-law bought a piece of property 15 years ago for $29,000. He j

Question

1) Your brother-in-law bought a piece of property 15 years ago for $29,000. He just sold it for $50,000, and spent the week-end bragging about his real-estate acumen. As a reality check, you tell him that his annual rate of return was:

7.0%

11.5%

3.7%

5.5%

2) Your client realizes the need to start a systematic savings program for retirement. Approximately how much will the person have to invest at the end of every year to accumulate a lump sum of $500,000 in 20 years if the investment portfolio is expected to earn 8.5% per year? (The client has zero dollars invested currently.)

$25,000

$9,348

$9,526

$10,335

3) Approximately how many years will it take an investor to accumulate $1,500,000 if the person currently has saved $450,000, they commit to investing $60,000 at the end of every year, and the portfolio is expected to earn a 12% return?

7 years

5 years

17 years

8 years

4) You believe that a 1974 Dodge Charger is going to be worth at least $20,000 is 5 years. If you could invest the same funds and receive a 12% annual return, how much would you be willing to pay for the car?

$11,000

$12,000

$11,350

$11,250

7.0%

11.5%

3.7%

5.5%

Explanation / Answer

1.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

50000=29000(1+r/100)^15

(50000/29000)^(1/15)=(1+r/100)

(1+r/100)=1.037

r=(1.037-1)*100

=3.7%(Approx).

2.

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

500,000=Annuity[(1.085)^20-1]/0.085

500,000=Annuity*48.37701323

Annuity=500,000/48.37701323

=$10335(Approx).

3.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

Hence A for $450,000=$450,000*(1.12)^n

Also:

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=$60000[(1.12)^n-1]/0.12

Hence

1,500,000=450,000*(1.12)^n+$60000[(1.12)^n-1]/0.12

1,500,000=450,000*(1.12)^n+$500,000[(1.12)^n-1]

1,500,000=450,000*(1.12)^n+$500,000(1.12)^n-500,000

(1,500,000+500,000)=(1.12)^n[450000+500,000]

(1.12)^n=2,000,000/950,000

Taking log on both sides;

n*log 1.12=log(2,000,000/950,000)

n=log(2,000,000/950,000)/log 1.12

=7 years(Approx).

4.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

20000=P(1.12)^5

P=20000/1.12^5

=20000*0.567426855

=$11350(Approx).

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