Financial Literacy — Interest and Budgeting

Warm-up

The two-offers dilemma, projected: "Your $1,000 summer earnings can sit in (a) a savings account at 4% per year, or (b) your cousin's 'investment' promising 'double in 5 years.' Which grows faster?" Compute the account: $1000 \times 1.04^5 \approx \$1{,}217$. The cousin promises $2,000. "So the cousin wins?" — pause — "What questions should you ask first?" (Risk. Guarantee. Getting it back at all.)

Grade 9 finance: simple and compound interest computed honestly, and return weighed against risk like an adult.

Explore

Interest laboratory: (1) simple interest builds the table by hand: $500 at 6% simple → +$30 every year, linear, $A = 500(1 + 0.06t)$; (2) compound interest builds ITS table: interest on the balance, so $500 \to 530 \to 561.80 \to \ldots$, each row ×1.06 — exponential, $A = 500(1.06)^t$; (3) the race graph: both curves from one axis — twins for two years, then compounding pulls away forever.

Then the budget clinic returns at Grade 9 scale: a part-time-job monthly budget with fixed/variable classification, a savings rate CHOSEN first, and one debt scenario (a \$300 phone on a payment plan at 20% — the true total computed, the "low monthly payment" spell broken).

Formalize

Formalize both interest models:

$A_{\text{simple}} = P(1 + rt) \qquad A_{\text{compound}} = P(1 + r)^t$

The structural read: simple interest is LINEAR (slope $Pr$ — same dollars every year); compound is EXPONENTIAL (multiplier $1+r$ — same PERCENT every year, growing dollars). Every lesson about lines vs exponentials this year replays here with money as the y-axis. Rule-of-thumb seeded: at rate $r$%, doubling takes roughly $\frac{72}{r}$ years.

Practice

Practice: one simple and one compound computation with tables; the race graphed for a chosen $P, r$; one doubling-time estimate via the 72 rule checked by table; one payment-plan autopsy (total paid vs sticker); one budget build with a defended savings rate.

Exit ticket: $800 at 5% for 10 years — simple vs compound totals. ($800(1.5) = \$1{,}200$; $800(1.05)^{10} \approx \$1{,}303$ — the gap IS the interest-on-interest.)

Exit ticket

Practice: one simple and one compound computation with tables; the race graphed for a chosen $P, r$; one doubling-time estimate via the 72 rule checked by table; one payment-plan autopsy (total paid vs sticker); one budget build with a defended savings rate.

Exit ticket: $800 at 5% for 10 years — simple vs compound totals. ($800(1.5) = \$1{,}200$; $800(1.05)^{10} \approx \$1{,}303$ — the gap IS the interest-on-interest.)