1. **Simple Interest** Definition: Simple interest is the interest calculated only on the principal amount. Formula: $I = P \times r \times t$ Symbols: $I$ = interest, $P$ = principal, $r$ = rate per year, $t$ = time in years Example: If $P=1000$, $r=0.05$, $t=3$, then $I=1000 \times 0.05 \times 3=150$. 2. **Compound Interest** Definition: Interest calculated on the principal and also on accumulated interest. Formula: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Symbols: $A$ = amount, $P$ = principal, $r$ = annual rate, $n$ = compounding periods per year, $t$ = years Example: $P=1000$, $r=0.05$, $n=4$, $t=3$, then $A=1000\left(1+\frac{0.05}{4}\right)^{12} \approx 1161.47$. 3. **Finding Interest Rate and Time in Compound Interest** Given $A$, $P$, $n$, and either $r$ or $t$, solve for the unknown. Example: If $A=1161.47$, $P=1000$, $n=4$, $t=3$, find $r$: $$1161.47 = 1000 \left(1 + \frac{r}{4}\right)^{12}$$ Solve for $r$: $$\left(1 + \frac{r}{4}\right)^{12} = 1.16147$$ $$1 + \frac{r}{4} = (1.16147)^{\frac{1}{12}} \approx 1.0125$$ $$\frac{r}{4} = 0.0125 \Rightarrow r = 0.05$$ 4. **Simple Annuity** Definition: Equal payments made at the end of each period. Formula for future value: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ Example: $P=100$, $r=0.05$, $n=3$, then $$FV = 100 \times \frac{(1.05)^3 - 1}{0.05} = 100 \times 3.1525 = 315.25$$ 5. **General Annuity** Definition: Payments made at regular intervals, can be at beginning or end. Formula varies; for payments at beginning (annuity due): $$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$ Example: $P=100$, $r=0.05$, $n=3$, then $$FV = 100 \times 3.1525 \times 1.05 = 331.01$$ 6. **Deferred Annuity** Definition: Annuity payments start after a delay. Formula: Calculate future value at start of payments, then discount back. Example: $P=100$, $r=0.05$, $n=3$, deferred 2 years. Calculate $FV$ at year 5: $$FV = 100 \times \frac{(1.05)^3 - 1}{0.05} = 315.25$$ Discount back 2 years: $$PV = \frac{315.25}{(1.05)^2} = 285.87$$ 7. **Stocks and Bonds** Stocks: Ownership shares in a company. Bonds: Debt instruments with fixed interest. Example: Bond with face value 1000, coupon rate 5%, pays annually. Annual interest = $1000 \times 0.05 = 50$. If bond price is 950, yield = $\frac{50}{950} \approx 0.0526$ or 5.26%.