Applications of Sequences and Series in Financial Mathematics

Vocabulary and key concepts regarding financial mathematics including asset value changes, types of interest, and loan terms as discussed in the lecture notes.

Appreciation

The increase in the value of an asset (like a house, land, or investment) over time, often occurring due to factors like demand, improvements, or inflation.

Depreciation

The decrease in the value of an asset over time, usually happening due to usage, aging, or becoming outdated.

Simple Interest

Interest that is computed only on the principal and then added to it.

Compound Interest

Interest that is computed on the principal and on the accumulated past interest.

Loan

Money borrowed from a bank or lender that must be paid back over time, usually with added interest.

Mortgage

A specific type of loan used to buy real estate (like a house or land) where the property itself is used as a guarantee (collateral) until the loan is fully paid.

Accumulated value

Also known as future value, it is the total amount an investment is worth after a certain time, including the original investment and all growth from appreciation or interest.

Conversion or Interest Period

The time between successive conversions of interest.

Frequency of conversion

The number of conversion periods in one year.

Rate

The yearly rate of increase of the investment.

Period Rate

The rate of interest for one conversion period.

Time of term

The duration, measured in years, for which the money is borrowed or invested.

Arithmetic Growth

A financial scenario where the value of an item increases by a fixed amount every year, modeled using an arithmetic sequence.

Arithmetic Sequence Formula

$$a_n = a_1 + (n-1)d$$

Geometric Growth

A financial scenario where the value of an item increases by a fixed percentage each year, modeled using a geometric sequence formula with a common ratio.

Geometric Sequence Formula

$$a_n = a_1 r^{n-1}$$

Common Ratio (r) in Geometric Growth

In the context of annual percentage increase, the ratio is calculated as $1 + r_{rate}$ (e.g., for a 5% increase, $r = 1.05$).