# Math 103 review final exam

Math 103

Review for Final Exam

Math 103

Review for Final Exam

v01

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?

(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?

(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?

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

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

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) =

Pages (550 words)
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