Finance

Compound Interest, Costs, Annuity Formulas and more

Interest: The fee paid in exchange for the right to borrow money. There are two main types of interest: Simple and Compound.

• Simple interest is a predetermined percentage of the principle that was initially lent to the borrower that the borrower must pay in exchange for access to the funds.

$$FV=PVrn$$

$FV$: Future Value
$PV$: Present value (Principal amount)
$r$: Interest Rate
$n$: number of periods

• Compound Interest is the interest that is paid that includes both principle and compounding interest (interest on top of the interest).

$$FV=PV*(1+\frac{r}{t})^{n*t}$$

$FV$: Future Value
$PV$: Present value (Principal amount)
$r$: Interest Rate
$n$: number of periods
$t$: times per period

Annuity: series of payments of a fixed amount for a specified number of periods.

• Regular Annuity: End ordinary annuity or annuity in arrears. (Paid at the end)
• Annuity Due: Beginning annuity due or annuity in advance (paid at the beginning).
• Deferred annuity: first payment is later than first period (paid first later).
• Perpetuities: annuities paid forever.

$$FV=PR*\frac{1+\frac{r}{t}^{n*t} -1}{\frac{r}{t}}$$

$FVA$: Future value Annuity $PVA$: Present value Annuity $PR$: Periodic value (value of each payment) $r$: Annuity Interest Rate $n$: number of periods $t$: times per period

References

• Fundamentals of Financial Management 13th Edition