FinanceCollege3 topic explainers

Finance Fundamentals course

Interest, annuities and loan payments.

Topics in this course

1.Simple and Compound Interest
Interest is the price of borrowing money, or the reward for lending it. Simple interest is paid only on the original principal: $I = Prt$ . Compound interest is paid on the principal plus interest already earned, so the balance grows faster and faster: $A = P\left(1 + \frac{r}{n}\right)^{nt}$ for $n$ compounding periods per year.
- Simple: $A = P(1 + rt)$ .
- Compound: $A = P(1 + \frac{r}{n})^{nt}$ ; continuous: $A = Pe^{rt}$ .
- Effective annual rate $= (1 + \frac{r}{n})^n - 1$ .
Quick check: Simple interest on $2,000 at 5% for 3 years.
$300
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study simple and compound interest
2.Time Value of Money
A dollar today is worth more than a dollar next year, because today's dollar can be invested to earn interest. The time value of money makes this precise. Future value grows a present amount forward: $FV = PV(1 + r)^n$ . Present value discounts a future amount back: $PV = \frac{FV}{(1 + r)^n}$ .
- $FV = PV(1 + r)^n$ and $PV = \frac{FV}{(1 + r)^n}$ .
- Annuity present value: $PV = PMT \cdot \frac{1 - (1 + r)^{-n}}{r}$ .
- NPV $= \sum \frac{CF_t}{(1 + r)^t} - \text{initial cost}$ .
Quick check: Future value of $1,000 at 5% for 3 years.
$1,157.63
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study time value of money
3.Loans and Amortization
Most car loans and mortgages are amortising loans: you pay the same amount every month, and each payment covers that month's interest first, with the rest reducing the principal. Early payments are mostly interest; later payments are mostly principal, because the balance the interest is charged on keeps falling.
- Payment: $M = P\frac{i(1 + i)^n}{(1 + i)^n - 1}$ , with $i$ the monthly rate and $n$ the number of payments.
- Each month: interest $= i \times$ balance; principal paid $= M -$ interest.
- Total interest $= nM - P$ .
Quick check: First-month interest on a $20,000 balance at 0.5% per month.
$100
Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study loans and amortization

Topics in this course

1.Simple and Compound Interest

2.Time Value of Money

3.Loans and Amortization

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