swerve wrote: ↑

Tue Jan 14, 2020 11:42 am

At the same time that Rick opened an account with $150 at Bank A, Mary Jane opened an account at Bank B with $150. Mary Jane’s account has 10% simple annual interest and Rick’s gives 12% annual interest compounded quarterly. If neither Rick nor Mary Jane make any additional deposits or withdrawals, then what percent more does Rick have in his account after a year?

A. \(\frac{150\cdot 1.03^4-150\cdot 1.1}{150\cdot 1.1}\)
B. \(150\cdot 0.12 \cdot 2 - 150 \cdot 0.1\cdot 2\)
C. \(\frac{150\cdot 0.12\cdot 4-150\cdot 0.1}{150\cdot 1.1}\)
D. \(150\cdot 1.03^4 - 150\cdot 1.1\)
E. \(\frac{150\cdot 1.12^4-150\cdot 1.1}{150\cdot 1.1}\)

The OA is A

After one year, Mary Jane has 150(1.1) dollars in her account, and Rick has (1 + 0.12/4)^4 = 150(1.03)^4 dollars in his account. Therefore, the amount Rick has after one year, is

[150(1.03)^4 - 150(1.1)] / [150(1.1)] x 100 percent more than Mary Jane’s.

Answer: A [Note: To be precise, it should be multiplied by 100]