Question

Carlos is looking at different savings account options to save for college. First Bank offers 1% interest compounded annually. Community Bank offers 2% simple interest. If Carlos is depositing $1,000 into the account for four years with no additional withdrawals or deposits, which bank is the better choice?

Answer 1

Community Bank

Explanation:

My teacher gave us the answer. :)

Answer 2

Community Bank is the better choice.

Explanation:

-We calculate the interest earned on the principal over 4 years for the different banks:

#First Bank, i=0.01, P=$1,000

`\#Calculate \ the \ effective \ interest \ rate.\\\\\\i_m=(1+i/m)^m-1=(1+0.01/1)^1-1=0.0100\\\\\therefore A=1000(1.01)^4=1040.60\\\\I=A-P=1040.60-1000=\$40.60`

Hence, the interest earned on the principal is $40.60

#Community Bank, i=0.02,P=$1,000, the interest earned, I, over 4 years is:

`I=PRT\\\\=1000* 0.02* 4\\\\=80.00`

The simple interest earned is greater than the compound interest earned:

`I_s>I_c\\\\\$80>\$40.60`

Hence, Community Bank is the better choice.