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1. For the cash flows shown, calculate the future worth in year 8 at i=10% per year.

Year 0 1 2 3 4 5 6 7

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Cash Flow, $ 500 500 500 0 800 800 800 800

F=500(F/A, 10%, 3)(F?P10%, 6)+800(F/A, 10%, 4)(F/P, 10%, 1)=7016

2. The operation expenses of a company are $550,000 this year (year 0) and will be $550,000 again in year 1, but then are estimated to increase by $40,000 each year through year 1 What is the equivalent annual worth in year 1 to 12 of the operation expenses at i=10% per year?

A=550,000+550,000(A/P, 10%, 12)+40,000(A/G, 10%, 12)=806254

3. At interest rate of 20%/year, how much money you must deposit for five consecutive years starting three years from now to accumulate $50,000 fifteen years from now?

X(P/A, 20%,5)(F/P,20%, 13)=50,000

X=1562

4. An engineering student plans to deposit $10,000 now and again after 3 years. Find total amount after 5 years at 12% per year, compounded quarterly.

i=12%/3=3%

F=10,000(F/P, 3%, 20)+10,000(F/P, 3%, 8)=30730

5. Given the following cash flow shown, what is the equivalent annual A over 8 years at i=10%/year?

Year 0 1 2 3 4 5 6 7 8

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Cash Flow, $ 0 0 0 0 50 50 50 50 50

A=50(P/A, 10%, 5)(P/F, 10%, 3)(A/P, 10%,10%,8)=26.7

6. Shark Loan Company makes emergency loans of up to $500 for 1 month for a fee of 4% the loan amount. If a person borrows $500, what is (a) the nominal interest rate per year, and (b) the effective rate per year?

1. r=4%*12=48%/year, c.m.
2. i=(1+.48/12)^12-1=0.601 or 60.1%

7. A company borrows $3.5 million now (year 0). If the company uses an interest rate of 16% per year, compounded quarterly, what is the uniform amount per quarter the company must make in order to recover the loan in three years?

n=3*4=12, i=16%/4=4%

A=3.5M(A/P,4%, 12)=0.373M

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