Annual Savings Program Ursula opens a -year CD that yields interest per year. She begins with a deposit of . At the end of each year when the CD matures, she reinvests at the same interest rate, also adding to the value of the CD from her other savings. (So for example, after the first year her CD has earned of in interest, for a value of at maturity. She then adds , or , bringing the total value of her renewed CD to .)
(a) Find a recursive formula for the amount in Ursula’s CD when reinvest at the end of the .
(b) Find the first five terms of the sequence . Does this appear to be a geometric sequence?
(c) Use the pattern you observed in (b) to find a formula for .
(d) How much has she saved after ?
A recursive formula for the amount in Ursula’s CD when amount is reinvested at the end of the .
An original deposit amount is and interest rate is per year.
Use distributive law.
An original deposit amount is and interest rate is per year, reinvest the same interest rate also adding to the value of the CD,
The first five terms of the sequence .
A formula for .
Saved amount after .
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