An Annuity Is a Sequence of Payments Made at Regular $n ^ { \text {th } }$

question 55

Short Answer

An annuity is a sequence of payments made at regular intervals. Suppose that a sum of $200 is deposited at the end of each month into an account earning interest at the rate of 12% per year compounded monthly. Then the amount on deposit at the end of the $n ^ { \text {th } }$ month is $f ( n ) = 20,000 \left[ ( 1.01 ) ^ { n } - 1 \right]$ .
Consider the sequence $\left\{ a _ { n } \right\}$ defined by $a _ { n } = f ( n )$ (a) Find the $24 ^ { \text {th } }$ term of the sequence, and interpret your result.
(b) Evaluate $\lim _ { n \rightarrow \infty } a _ { n } ,$ and interpret your result.

---

Definitions:

Fixed Price

A set price that does not change, regardless of variations in market conditions or costs of production.

UCC

An extensive assembly of legal norms, the Uniform Commercial Code, presides over the entirety of commercial exchanges in the United States.

Merchant

An entity that sells goods or services in exchange for money, usually within the retail or business-to-business markets.

UCC Applies

Refers to situations where the Uniform Commercial Code, a set of laws governing commercial transactions in the United States, is applicable.