Model and solve problems involving compound interest, depreciation, annuities, loans and investments using recursion and the financial solver.

What this dot point is asking

You must recognise compound interest, depreciation, loans and annuities as one family of recurrence relations, set up the correct sign on the payment, and solve with recursion or the finance solver.

One recurrence for every model

The whole topic reduces to choosing $R$ and $d$ in the same recurrence.

The sign of $d$ is the decision that separates a loan from a savings plan. A repayment is subtracted, a deposit is added.

Converting the rate

Interest is quoted as a nominal annual rate but applied per compounding period. Divide by the number of periods per year: monthly uses $\dfrac{\text{rate}}{12}$, quarterly $\dfrac{\text{rate}}{4}$. Then count $n$ in those same periods.

Using the finance solver

The SCSA calculator-assumed section expects the built-in finance (TVM) solver for harder questions. The standard fields are present value $PV$, future value $FV$, payment $PMT$, number of periods $N$ and interest rate per year $I\%$ with a compounding setting. Sign convention: money you receive is positive, money you pay is negative. To find an unknown payment or the number of periods, enter the four known values and solve for the fifth.

For the loan above, set $PV = 10000$, $I\% = 12$, compounding monthly, $PMT = -900$ and solve for $N$ to find the number of payments, then read the final small payment from the last balance.

Which tool for which question

The topic rewards picking the efficient method. For a single balance a few periods ahead, iterate the recurrence by hand. For a balance many periods ahead with no payments, use the explicit form $A_n = A_0 R^n$. For an unknown payment, number of periods, or present or future value in a loan or annuity, use the finance solver. For "when does the balance first reach a target", iterate (or solve for $N$) and round to the next whole period. Recognising which of these a question wants saves time and avoids setting up the wrong calculation.

Reading the wording for sign and rate

Two reading skills decide every finance answer. First, the sign of the regular payment: words like "repay", "withdraw" and "pay off" mean a subtraction (negative $d$); words like "deposit", "contribute" and "add" mean an addition (positive $d$). Second, the compounding period: "compounding monthly" with an annual rate means divide by $12$ and count months; "quarterly" means divide by $4$ and count quarters. Get these two right and the rest of the calculation is mechanical; get either wrong and the whole answer is off.