Time value of money practice problems that never repeat
Most finance practice sets have a fixed list of problems and an answer key. You work through them once, remember that the mortgage question comes out to $1,264.14, and the second time through you are recalling, not calculating. Ratedrill was built around one rule: every attempt gets fresh numbers, so the only way through a problem is the method.
Each of the 53 problem types is a template. Every attempt picks new, realistic inputs: a new loan amount, rate or term, a new set of cash flows, a new bond coupon. Press New numbers and you get another version of the same problem whenever you like. That is the difference between recognizing a formula and being able to use it in an exam or at a client's desk.
Finance math practice, right in your browser
There is nothing to install and no spreadsheet template to download. Each problem states the scenario and how to round, you enter one number, and the check tells you at once whether it is right. Money answers count when they are within one cent or 0.01%, whichever is larger, and rates count within 0.01 percentage points.
Use whatever tool you like: a financial calculator, Excel, Google Sheets or a pencil and the formula. Every worked solution shows all three, so you can check your method against the one you will use at work.
TVM practice built in five levels
The 53 problem types are organized into levels, and each level only adds one or two ideas on top of what you already know.
- Basics: simple interest, future and present value of a lump sum, monthly compounding, the return or years needed to reach a goal, exact time to double, effective rates from a monthly or daily APR, continuous compounding.
- Annuities: future value of a savings plan, present value of a payment stream, annuity due, the monthly saving to reach a goal, perpetuities and growing perpetuities, growing and deferred annuities, how long a balance lasts.
- Loans: mortgage and car payments, the balance after k payments, total interest, the interest and principal parts of payment k, payoff time with extra payments, a balloon payment, the APR implied by a payment, how much you can borrow.
- Investments: NPV, IRR, payback and discounted payback, profitability index, bond price, yield to maturity, current yield, holding period return and compound annual growth rate.
- Business math: break-even units and revenue, price for a target margin, margin from a markup, the cost of skipping an early-payment discount, straight-line, double-declining and sum-of-the-years'-digits depreciation, real return after inflation, WACC and the after-tax cost of debt.
Within a level the problems get harder one notch at a time. By the end of Loans you have split payment k into interest and principal, worked out when extra payments clear the balance and backed out the APR behind an advertised payment, not because you read about it, but because the problem would not pass until you did.
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Annuity practice problems and loan amortization practice
Annuities and loans are where most time value of money mistakes happen, because the same four mistakes keep coming back. The checker names them.
- The sign convention: a payment out and a value in must have opposite signs, or the calculator returns nonsense.
- The factor of 12: an annual rate with monthly payments needs a monthly rate and a monthly term, both of them.
- Timing: an annuity due pays at the start of the period, an ordinary annuity at the end, and the answers differ by one period of interest.
- Early rounding: rounding the monthly rate to two decimals before the last step moves a 30-year mortgage payment by dollars, not cents.
NPV and IRR practice for project decisions
The Investments level covers the numbers behind every capital budgeting decision: net present value at a stated discount rate, internal rate of return, payback and discounted payback, and the profitability index, each on a fresh set of cash flows. Then the bond side of the same math: price from the coupon and yield, yield to maturity from the price, and current yield.
Each worked solution shows the cash flow timeline, the formula with the numbers filled in, the calculator keystrokes and the matching Excel function, such as NPV, IRR or RATE, so the method transfers to whatever you use at work.
Financial calculator practice, keystroke by keystroke
If your course or exam expects a financial calculator, every worked solution lists the TVM keystrokes: N, I/Y, PV, PMT and FV with the sign convention, and which key to compute. If you use Excel instead, the same solution shows the formula, from PV, FV, PMT and NPER to NPV, IRR, RATE and EFFECT. If you prefer the formula itself, it is there too, with the numbers substituted.
Seeing all three side by side is the fastest way to stop mixing them up, and the fastest way to switch tools when an exam allows one and your job uses another.
Learn the math of money by getting it wrong first
A hint is one click away, but the worked answer opens only after your second attempt. That is on purpose. Entering a number, seeing it marked off, reading that the likely mistake is a sign error, and fixing it yourself is the part that sticks. Copying a solution before you have tried does not.
Every problem also explains the idea behind it: why a growing perpetuity divides by the rate minus the growth, why the effective rate is higher than the APR, why skipping a 2/10 net 30 discount costs far more than two percent a year.
Finance exam practice and timed problems
Business and finance courses, the CFA Level I quantitative section, banking and lending exams and analyst assessments all test this math under time pressure. Ratedrill's timed mode puts a clock on each problem with hints and answers locked until time is up, and fresh numbers mean you cannot coast on a remembered result.
Run through the first three levels in the week before an exam, with New numbers for the types that give you trouble, and the questions will feel like problems you have already done.
Try a timed problem
Time value of money practice for students, bankers and business owners
If you have never computed a present value, the Basics level starts with simple interest and does not assume anything. If you work with money every day, skip to Loans, Investments or Business math and look for the gaps: most people have one calculation they have always looked up, and fresh numbers find it quickly.
Every problem type is independent, so you can jump to the one you need for today's question and come back to the rest later.
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