# Normal Distribution, Time Value of Money

1.Consider the normal distributions drawn below (with different scales)

They both have m = 20 and the area of the shaded region of each is 0.90. Which of the following holds?

a. x1 < x2

b. x1 > x2

c. x1 = x2

d. There is not enough information

e. x1 >= x2

2.If you deposit $5000 into a fund paying 6% interest compounded quarterly, how much can you withdraw at the end of each quarter for 5 years?

a. $135.92

b. $970.45

c. $291.23

d. $215.17

e. none of the above

Please see the attached file for full problem description.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1.Consider the normal distributions drawn below (with different scales)

They both have m = 20 and the area of the shaded region of each is 0.90. Which of the following holds?

a. x1 < x2

b. x1 > x2

c. x1 = x2

d. There is not enough information

e. x1 >= x2

Answer: a. x1 < x2

The standard deviation for b) s= 8 is greater than that of a) s= 5.

This means that the spread around the mean is more for b) than for a)

Thus x2 is farther from mean = M = 20.00

Thus x1 < x2

We can also calculate the numerical values of x1 and x2

For x1

Mean=M = 20.00

Standard deviation =s= 5.00

Z corresponding to 90% is 1.2816

z=(x-M )/s or x=M +z*s

or x1=20+1.2816*5= 26.41

For x2

Mean=M = 20.00

Standard deviation =s= 8.00

Z corresponding to 90% is 1.2816

z=(x-M )/s or x=M +z*s

or x2=20+1.2816*8= 30.25

Therefore a. x1 < x2

2.If you deposit $5000 into a fund paying 6% interest compounded quarterly, how much can you withdraw at the end of each quarter for 5 years?

a. $135.92

b. $970.45

c. $291.23

d. $215.17

e. none of the above

Answer: c. $291.23

To calculate the amount that can be withdrawn each quarter we need to know PVIFA (Present Value Interest Factor for an Annuity)

Withdrawal Q Quarterly

No of years= 5

No of Periods= 20 (=5 x 4 quarters per year)

Discount rate annually= 6.00% annual

Discount rate per period= 1.5% (= 6%/4)

n= 20

r= 1.5%

PVIFA (20 periods, 1.5% rate=) 17.1686 (From the tables)

Withdrawal (equal amount for each quarter):

Present Value= 5,000 (The amount deposited at time t=0)

Therefore

withdrawal: 291.23 =5000/17.1686

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