with Worked Solutions and Rationales 2026/2027
Practice questions
Attempt each numbered item using its case assumptions. Show the formula,
substitution, units, and interpretation. Unless the case states otherwise, round final
currency to two decimal places and retain unrounded intermediate values. Questions
within a case share its stated data.
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.
2. Find the simple-interest ending value.
3. Find the annually compounded ending value.
4. Find the additional earnings from annual compounding.
5. Find the total compounded holding-period return.
,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.
7. Find the future value of $5,000 after 4 years.
8. How long does it take to double at 8% with annual compounding?
9. What annual effective return doubles money in 5 years?
10. At 8%, what is the opportunity cost today of receiving $15,000 in year 4 rather
than now?
,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.
12. Find the effective annual rate of the monthly account.
13. Find the value of $1,000 after 24 months in the monthly account.
14. Which account yields more over one year?
15. What monthly rate is equivalent to 12% effective annually?
, 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.
17. Find ordinary-annuity future value at year 5.
18. Find annuity-due present value at time 0.
19. Find annuity-due future value at year 5.
20. How much more is the due annuity worth today?