Question

Aerial's grandmother gave her $5,500.00 to save for her college education. She went to the bank to open a savings account. The bank told her they had two options available.

Account A will pay 5.5% simple interest until the account is closed.

Account B will pay 4.5% simple interest and if the account is left open for longer than 3 years, then at the end of the third year a bonus account will be opened with $250 that also earns 4.5% for the remainder of the time the initial account is open. When the initial account is closed, the bonus account will be closed as well and the money from the two accounts will be combined.

If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account a or b is the better choice earning her ________ more.

A.) 18.75
B.) 30.00
C.) 41.25
D.) 208.75
E.) 220.00

Answer 1

In case of the first account or account A:
Amount earned = Principal (1 + Rate * Time)
= 5500( 1 + 0.055 * 4)
= 5500( 1 + 0.22)
= 5500 * 1.22
= 6710 dollars
Interest earned = 6810 - 5500
= 1210 dollars
In case of account B

First case:
Amount = Principal (1 + Rate * Time)
= 5500 ( 1 + 0.045 * 4)
= 5500 * 1.18
= 6490 dollars
Interest earned = 6490 - 5500
= 990 dollars
Second case:
Amount = Principal (1 + Rate * Time)
= 250 ( 1 + 0.045 * 1)
= 250 * 1.045
= 261.25 dollars
Total interest earned = 990 + 261.25
= 1251.25 dollars

Difference in interest earned = 1251.25 - 1210
= 41.25 dollars

f Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account b is the better choice earning her $41.25 more. The correct option is option "C".

Answer 2

The correct option is C.) $41.25

The better choice is Account B

Explanation:

Principal = $5500 , Time = 4 years

Amount earned in Account A :

Rate = 5.5% = 0.055

Interest = Principal × Rate × Time

= 5500 × 0.055 × 4

= $1210

Amount earned = Principal + Interest

= 1210 + 5500

= $6710

In case of account B

First case :

Rate = 4.5% = 0.045

Interest = Principal × Rate × Time

= 5500 × 0.045 × 4

= $990

Amount earned = Principal + Interest

= 990 + 5500

= $6490

Second case :

Time = 1 year , Principal = $250

Interest = Principal × Rate × Time

= 250 × 0.045 × 1

= $11.25

Amount earned = Principal + Interest

= 250 + 11.25

= $261.25

Total amount earned through Account B = 6490 + 261.25

= $6751.25

Therefore, Amount earned in Account B is more as compared to amount earned through Account A

Amount which is earned more through Account B = 6751.25 - 6710

= $41.25

Hence, The correct option is C.) $41.25

Also, The better choice is Account B