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.

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