Simple interest · Key concepts
Cards
01What does the principal of a loan represent?
The original amount borrowed
Principal is the amount on which the loan's interest is calculated; maturity value includes interest.
Slater, Ch. 16, pp. 425-42602In simple interest, interest is calculated on which base?
The original principal, unless a payment reduces it
Simple interest does not automatically earn interest on prior interest; the U.S. Rule adjusts principal after qualifying payments.
Slater, Ch. 16, pp. 426, 431-43303Which formula gives simple interest?
I = PRT
Multiply principal by the annual rate and time in years.
Slater, Ch. 16, pp. 42604Which formula gives maturity value for a simple interest loan with no partial payments?
M = P + I
At maturity, the borrower repays the principal and the interest owed.
Slater, Ch. 16, pp. 425-42605With an annual rate, how should a term stated in months be entered into I = PRT?
Months divided by 12
Dividing by 12 converts months to a fraction of a year.
Slater, Ch. 16, pp. 426-42706Which denominator does the chapter use for exact interest?
365
The textbook's exact-interest convention uses actual elapsed days divided by 365.
Slater, Ch. 16, pp. 42707Which denominator does the chapter use for ordinary interest?
360
Ordinary interest uses an assumed 360-day year.
Slater, Ch. 16, pp. 427-42808What combination defines the Banker's Rule used in this chapter?
Actual elapsed days with a 360-day year
The chapter calls ordinary interest based on actual elapsed days the Banker's Rule.
Slater, Ch. 16, pp. 427-42809How are the loan's starting and repayment dates counted?
Exclude the starting date; include the repayment date
This convention measures the actual elapsed days and prevents an extra day of interest.
Slater, Ch. 16, pp. 42710For the same positive principal, rate, and actual number of days, which method gives more interest?
Ordinary interest
Dividing by 360 gives a larger time fraction than dividing by 365.
Slater, Ch. 16, pp. 427-42811How is an annual rate of 7.5% written as a decimal in a formula?
0.075
Divide a percentage by 100 before multiplication.
Slater, Ch. 16, pp. 42612What should you generally do with intermediate values in a simple-interest calculation?
Keep full precision until the final answer
Premature rounding of time or a denominator can change the final interest or inferred principal.
Slater, Ch. 16, pp. 426, 428-43113Given interest, rate, and time, which formula finds principal?
P = I / (RT)
Rearrange I = PRT by dividing both sides by RT.
Slater, Ch. 16, pp. 429-43014Given interest, principal, and time, which formula finds annual rate?
R = I / (PT)
Divide interest by principal times time in years, then convert the resulting decimal to percent.
Slater, Ch. 16, pp. 43015Given interest, principal, and annual rate, which formula finds time in years?
T = I / (PR)
Dividing by principal times annual rate gives time in years.
Slater, Ch. 16, pp. 430-43116After finding T in years, how do you find the total ordinary-interest days?
Multiply the entire T by 360
Every year represents 360 days under this convention; whole years must also be included when total days are requested.
Slater, Ch. 16, pp. 430-43117A computed term is 42.01 days. Under the chapter's whole-day rule, which term is reported?
43 days
The chapter rounds any fraction of a day upward to a full day.
Slater, Ch. 16, pp. 43118A computed term is exactly 42 days. What is the reported term?
42 days
Rounding up adds a day only when a genuine fractional day remains.
Slater, Ch. 16, pp. 43119With principal and time fixed, what happens to simple interest when the rate doubles?
Interest doubles
I = PRT is directly proportional to R when P and T are fixed.
Slater, Ch. 16, pp. 42620With a positive rate and unchanged principal, what happens to simple interest when time triples?
Interest triples
Simple interest grows linearly with time for a fixed principal and rate.
Slater, Ch. 16, pp. 426-42721Why is a nine-month loan at an annual rate not treated as nine years?
The time unit must match the annual rate
The annual rate requires T = 9/12, not T = 9.
Slater, Ch. 16, pp. 426-42722If maturity value and principal are known, how do you find interest?
I = M - P
Maturity value contains principal plus interest, so subtract principal.
Slater, Ch. 16, pp. 425-42623If principal and interest are both positive, how does maturity value compare with principal?
Maturity value is greater
M = P + I adds a positive charge to principal.
Slater, Ch. 16, pp. 425-42624Under the U.S. Rule, what does a partial payment cover first?
Accrued interest
The rule allocates the payment to interest already earned before reducing principal.
Slater, Ch. 16, pp. 431-43225Under the U.S. Rule, what happens to the part of a payment left after accrued interest is covered?
It reduces principal
The unused portion of the payment is a principal reduction.
Slater, Ch. 16, pp. 431-43226After a partial payment reduces principal, what base is used for the next interval's interest?
The adjusted principal balance
Future simple interest is calculated on the remaining principal for the next interval.
Slater, Ch. 16, pp. 432-43327What time is used for the second interest interval in a U.S. Rule schedule?
Time since the previous payment
Each interval starts where the previous one ended; using cumulative days repeatedly double-counts time.
Slater, Ch. 16, pp. 432-43328At maturity after partial payments, what must still be paid?
Adjusted principal plus interest since the last payment
The final payoff includes the remaining principal and the last accrued interest.
Slater, Ch. 16, pp. 43329How is total interest found from a U.S. Rule schedule?
Add the interest from all intervals
Every interval's interest is a borrowing cost, including interest already covered by earlier payments.
Slater, Ch. 16, pp. 432-43330When does the chapter's U.S. Rule example round interest?
At each payment interval, to cents
The worked U.S. Rule procedure rounds each interval's interest to cents before updating the balance.
Slater, Ch. 16, pp. 432-43331A partial payment exactly equals the interest accrued. What happens to principal?
It stays unchanged
All of the payment is used for interest, leaving no amount to reduce principal.
Slater, Ch. 16, pp. 431-43232For the same loan and payment amount, why can paying earlier reduce total interest?
Principal is reduced sooner
An earlier reduction leaves a smaller interest base over more of the remaining term.
Slater, Ch. 16, pp. 431-43333Which action overstates the principal reduction from a partial payment?
Subtracting the entire payment from principal without covering interest first
Part of the payment belongs to accrued interest, so the full payment cannot all reduce principal.
Slater, Ch. 16, pp. 431-43334What does the adjusted balance mean immediately after a qualifying U.S. Rule payment?
The remaining principal
After interest is paid, the remaining payment reduces principal and produces the adjusted balance.
Slater, Ch. 16, pp. 432-43335How should you verify a principal found from I / (RT)?
Substitute it into I = PRT
Substitution should reproduce the given interest, allowing for final rounding.
Slater, Ch. 16, pp. 429-43036Under the chapter's stated exact-interest convention, what changes when elapsed dates include February 29?
The actual day count includes that day
Actual elapsed days include leap day; this study set keeps the chapter's specified 365-day denominator.
Slater, Ch. 16, pp. 427, 43837Why is ordinary interest not automatically a 30-days-per-month calculation here?
The numerator still uses actual calendar days
A 360-day denominator does not replace the actual elapsed-day count with assumed months.
Slater, Ch. 16, pp. 427-42838If a simple-interest loan has zero interest rate and no fees, what is its maturity value?
The principal
With R = 0, I = PRT is zero, so M = P.
Slater, Ch. 16, pp. 425-42639If a problem asks for the annual rate, why is interest divided only by principal insufficient for a partial year?
That gives the return for the term, not an annualized rate
The rate formula also divides by time in years to annualize the interest cost.
Slater, Ch. 16, pp. 43040Which expression correctly recovers principal from maturity value, annual simple rate, and time?
P = M / (1 + RT)
Starting from M = P(1 + RT), divide by the whole growth factor.
Slater, Ch. 16, pp. 425-426