Algebra 2 Problems of the Day (Algebra 2 Regents, August 2024 Part IV)

This exam was adminstered in August 2024 .

August 2024 Algebra 2, Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.

37. Taylor wants to open an investment account with the $1200 she received for her birthday. She has narrowed her choices down to two banks. America’s Bank offers 6.4% annual interest compounded quarterly. Barnyard Bank offers 6.35% annual interest compounded continuously.

Write functions for A(t) and B(t) to represent the value of her investment with America’s Bank and Barnyard Bank as a function of time, t, in years.

Taylor would like to invest the $1200 into one bank for ten years making no additional deposits and no withdrawals. With which bank will Taylor earn the most money? Justify your answer.

Taylor chooses to invest her money in Barnyard Bank. Algebraically determine how long, to the nearest tenth of a year, it will take her initial investment to triple assuming she makes no deposits or withdrawals.
Justify your answer.

Answer:

Compounded quarterly means four times a year. Compounded continuously means you have to use e.

A(t) = 1200(1 + 0.064/4)^4t
B(t) = 1200e^0.0635t

A(10) = 1200(1 + 0.064/4)⁴⁽¹⁰⁾ = 2264.277...
B(t) = 1200e^0.0635(10) = 2264.426...

After 10 years, Barnyard Bank will earn more money.

Triple $1200 is $3600. Some for B(t) = 3600.

3600 = 1200e^0.0635t
3 = e^0.0635t
ln 3 = 0.0635t
ln 3 / 0.0635 = t

t = 17.301...

It will take 17.3 years for the investment to triple.

End of Exam

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