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

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(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

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(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:

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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) =