Practice Problems with Worked Solutions & Rationales 2026/2027
Practice case 1
Simple and compound growth
Invest $10,000 for 3 years at a stated annual rate of 6%. Compare simple interest with
annual compounding. There are no withdrawals, taxes, or fees.
1. Find simple-interest earnings.
Working or response
2. Find the simple-interest ending value.
Working or response
3. Find the annually compounded ending value.
Working or response
4. Find the additional earnings from annual compounding.
Working or response
5. Find the total compounded holding-period return.
Working or response
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,Practice case 2
Lump sum valuation
Use an 8% annual effective rate and end-of-year timing unless a question gives
another horizon. No cash flows occur between the stated beginning and ending values.
6. Find the present value of $15,000 due in 4 years.
Working or response
7. Find the future value of $5,000 after 4 years.
Working or response
8. How long does it take to double at 8% with annual compounding?
Working or response
9. What annual effective return doubles money in 5 years?
Working or response
10. At 8%, what is the opportunity cost today of receiving $15,000 in year 4
rather than now?
Working or response
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,Practice case 3
Nominal and effective rates
A savings account quotes nominal APR 12%, compounded monthly. Another account
pays 12% effective annually. Assume deposits are made now and no fees or taxes
apply.
11. Find the monthly periodic rate.
Working or response
12. Find the effective annual rate of the monthly account.
Working or response
13. Find the value of $1,000 after 24 months in the monthly account.
Working or response
14. Which account yields more over one year?
Working or response
15. What monthly rate is equivalent to 12% effective annually?
Working or response
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, Practice case 4
Ordinary annuity and annuity due
Five equal payments of $2,000 occur annually. The effective annual rate is 8%.
Ordinary-annuity payments occur at years 1 through 5; annuity-due payments occur at
years 0 through 4.
16. Find ordinary-annuity present value at time 0.
Working or response
17. Find ordinary-annuity future value at year 5.
Working or response
18. Find annuity-due present value at time 0.
Working or response
19. Find annuity-due future value at year 5.
Working or response
20. How much more is the due annuity worth today?
Working or response
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