Math 103 review final exam

 

Math 103

 

 

 

Review for Final Exam

 

 

 

 

Math 103

 

Review for Final Exam

 

 

v01

 

 

1. Please simplify your answers as far as possible without a calculator. You may leave your answers

 

in terms of exponential and logarithmic expressions.

 

(a) John invests $5,000 in an account with semi-annual compounding and an annual interest

 

rate of 4%. How much money will he have after 35 years?

Answer with units:

(b) $7000 was deposited in a bank account earning 5.5% interest compounded continuously.

 

How long will it take for the amount in the account to double?

Answer with units:

(c) Assume that the yearly rate of price ination for housing in the the next ten years is 3.5%

 

and assume that this is compounded annually. A house costing $780,000 today will cost

 

more in ten years. How much will it cost in ten years?

Answer with units:

2. (a) What is the yield on a investment earning 10% compounded continuously? One of the

 

following calculations will help you answer the question. Circle the calculation that helps.

 

Yield (as a percentage):

(1:10)2 = 1:2100 (1:05)2 = 1:1025 (1:025)4 = 1:1038

 

e0:10 = 1:1052 e0:05 = 1:0513 e1:10 = 3:0042

 

 

2

 

(b) What is the present value of a cash ow of $1000 per year at a rate of 4%?

 

Present value (with units):

 

(c) What is the yield on a investment earning 8% compounded quarterly? One of the following

 

calculations will help you answer the question. Circle the calculation that helps.

 

Yield (as a percentage):

(1:08)4 = 1:3605 (1:04)2 = 1:0816 (1:02)4 = 1:0824

 

e0:08 = 1:0833 4e:02 = 4:0808 e1:08 = 2:9447

 

 

3

 

(d) What is the yearly cash ow from a perpetuity with a present value of $200,000. The annual

 

rate of return is 8%.

 

Yearly cash ow (with units):

 

3. Grandpa Bill wants to buy an outdoor playground set with a swing and slide for his grandkids.

 

That set costs $550 now. If he waits 2 years to buy it, how much will it cost if the yearly ination

 

rate for these playground sets is 5%?

Summary:

4

4. The cost (in dollars) to produce x oor tiles is

 

C(x) = 1500 + 2:50x:

 

Graph the cost function. Your graph should show the missing ticks marks and the y-intercept.

 

 

 

0 100 200 300 400 500 600 700 800 900 1000

 

0 Number of tiles

 

?

 

?

 

?

 

?

 

?

 

3000

 

?

 

?

 

Cost in dollars

 

 

5. The graph of f(x) =

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