New: the student classroom — explore compound interest, growth and depreciation, and regular savings with step-by-step investigations.
Compound Interest Tools
Print compound interest practice questions and worked answers, including a reverse-interest problem-solving extension.
Worksheets
Download worksheet PDF with answers
Use these questions for classroom practice, home learning or checking your understanding.
Open the calculator to check answers, download tables and copy an Excel formula.
Reverse interest extension
Go beyond substituting into a formula: compare rate conventions, repair incorrect reasoning and decide when a single-deposit model does not apply. Suitable for learners already comfortable with percentages, powers and rearranging formulas; no curriculum or examination-board alignment is claimed.
Student questions PDF (2 pages) Worked answers PDF (2 pages)
The student version has working space and no answers. The separate answer version explains each method and misconception. Both use A4 pages; choose “fit to page” for US Letter. No sign-up is required.
Assumptions: Except for the explicit extension in question 8, use one starting deposit with no later deposits or withdrawals. Rates are constant; ignore tax, fees and inflation. Amounts are in currency units (the same maths applies to pounds, dollars or euros). Do not round intermediate calculations. Round final money answers to two decimal places, except where a minimum deposit is requested.
Formula: A = P(1 + r/n)nt, so P = A/(1 + r/n)nt. A is the target, P the initial principal, r the nominal annual rate as a decimal, n the periods per year and t the years. With an effective annual rate e, use P = A/(1 + e)t.
Teaching sequence: Questions 1–2 build the method; 3 compares nominal and effective rates; 4–5 diagnose common errors; 6 tests minimum-deposit rounding; 7 checks zero interest; 8 extends the model to later deposits. Ask learners to predict whether P should be less than A before calculating.
An account grows to 1,210.00 after two years at 10% a year, compounded annually. Find the original deposit. Check your answer by growing it forwards.
P = 1,210 / 1.10^2 = 1,000.00. Forward check: 1,000 x 1.10 x 1.10 = 1,210.00. Dividing by the growth multiplier reverses the two increases.
A balance must reach 18,000.00 in five years at a nominal annual rate of 4.8%, compounded monthly. Write the monthly rate and number of periods, then find the starting deposit.
Monthly rate i = 0.048 / 12 = 0.004 (0.4%). There are 12 x 5 = 60 periods. P = 18,000 / 1.004^60 = 14,166.081516... = 14,166.08. Using the unrounded principal gives a forward balance of exactly 18,000; rounding the principal can leave a small difference.
To reach 10,000.00 in three years, compare (A) 6% nominal annual interest compounded monthly with (B) a 6% effective annual rate. Find each starting deposit. Which needs less, and why?
A: P = 10,000 / (1 + 0.06/12)^36 = 8,356.45. B: P = 10,000 / 1.06^3 = 8,396.19. A needs 39.74 less (difference calculated before rounding). Its effective annual growth is (1.005^12 - 1) x 100 = 6.1678...%, above 6%. Do not divide the effective annual rate by 12; an equivalent monthly rate is 1.06^(1/12) - 1.
A balance is 9,261.00 after three years at 5% a year, compounded annually. Sam says: 'Subtract 15% from the final balance: 9,261 x 0.85 = 7,871.85.' Explain two problems with Sam's method and find the correct principal.
Three 5% increases multiply by 1.05^3, not by 1.15: each increase applies to the new balance. Also, undoing a percentage increase means dividing by its multiplier, not subtracting that percentage from the final amount. P = 9,261 / 1.05^3 = 8,000.00. Check: 8,000 x 1.05^3 = 9,261.00.
For a target of 15,000.00 in two years at 3.6% nominal annual interest compounded monthly, Lee writes P = 15,000 / (1 + 3.6/12)^2. Identify and correct both errors, then calculate P.
Use the decimal rate 0.036, not 3.6. The exponent must count monthly periods: 12 x 2 = 24, not 2. P = 15,000 / (1 + 0.036/12)^24 = 15,000 / 1.003^24 = 13,959.47.
Find the minimum deposit in whole cents needed to reach at least 5,000.00 after five years at 4% a year, compounded annually. Interest is not rounded during the calculation. Would rounding to the nearest cent always guarantee the target? Explain.
Unrounded P = 5,000 / 1.04^5 = 4,109.635533... . Round UP to the next cent: 4,109.64. A deposit of 4,109.63 grows to 4,999.993267... (below the target); 4,109.64 grows to 5,000.005433... (above it). This comparison uses unrounded balances, not their displayed two-decimal values. Real accounts may round interest differently. Nearest-cent rounding happens to give the same answer here, but would fail whenever it rounds the required principal down. A minimum requires rounding up.
The target is 7,500.00 after four years. The annual rate is 0%, with no other cash flows. Find P and explain what happens to the reverse-interest formula.
P = 7,500 / (1 + 0)^4 = 7,500.00. The growth multiplier is 1, so there is no interest and the starting and ending amounts are equal. There is no need to divide by the rate.
A target of 12,000.00 in three years has a nominal annual rate of 6%, compounded monthly, AND deposits of 100.00 at each month-end. Can P = 12,000 / 1.005^36 be used unchanged? Explain, then find P using S = 100 x (1.005^36 - 1) / 0.005 as the future value of the monthly deposits.
No. The target includes growth from later deposits as well as the initial deposit. S = 3,933.610496... . Subtract that future value first: P = (12,000 - S) / 1.005^36 = 6,740.64. The check is P x 1.005^36 + S = 12,000 using unrounded P. This extension requires a cash-flow model; the site's reverse calculator is for a single starting deposit, so use the main calculator for this question.
Check the single-deposit questions with the reverse compound interest calculator, selecting the matching rate type and compounding frequency. Question 8 needs the main calculator with monthly deposits. See the compound interest formula guide for more context.
Resource updated . Educational examples only, not personal financial advice. Real accounts can use different rounding and interest-crediting rules.
Use the full calculator to include deposits, withdrawals, inflation, tax, fees, charts and downloadable tables.
FAQ