Ben deposits $1,750 into each of two savings accounts.
• Account I earns 2.75% annual simple interest.
• Account II earns 2.75% interest compounded annually.
Ben does not make any additional deposits or withdrawals. Which amount is closest to the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years?
A. $96.25
B. $1.32
C. $97.57
D. $193.82
Using the simple interest formula, the interest Ben will earn in Account I after 2 years is:
$1,750 x 0.0275 x 2 = $96.25
Using the compound interest formula, the interest Ben will earn in Account II after 2 years is:
$1,750 x (1 + 0.0275)^2 - $1,750 = $97.57
The difference between the two amounts is:
$97.57 - $96.25 = $1.32 (rounded to the nearest cent)
Therefore, the answer is B. $1.32
To find the difference between the interest earned in Account I and Account II, we need to calculate the interest earned in each account separately.
For Account I, which earns simple interest, we can use the formula:
Simple Interest = Principal * Rate * Time
Principal = $1,750
Rate = 2.75% = 0.0275 (expressed as a decimal)
Time = 2 years
Interest in Account I = $1,750 * 0.0275 * 2 = $96.25
For Account II, which earns compound interest, we can use the formula:
Compound Interest = Principal * (1 + Rate)^Time - Principal
Principal = $1,750
Rate = 2.75% = 0.0275 (expressed as a decimal)
Time = 2 years
Interest in Account II = $1,750 * (1 + 0.0275)^2 - $1,750
Calculating this:
Interest in Account II = $1,750 * (1.0275)^2 - $1,750 = $1,750 * 1.05500625 - $1,750 = $1,965.009375 - $1,750 = $215.009375
Finally, we find the difference between the interest earned in Account I and Account II:
Difference = Interest in Account I - Interest in Account II = $96.25 - $215.009375 = -$118.759375
Since the question asks for the amount closest to the difference, we determine that the closest amount is $97.57, which is option C.
To find the difference in interest earned between Account I and Account II at the end of 2 years, we need to calculate the interest earned in each account separately.
For Account I, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
Principal for Account I = $1,750
Rate for Account I = 2.75% = 0.0275 (as a decimal)
Time for Account I = 2 years
Interest for Account I = $1,750 * 0.0275 * 2
Interest for Account I = $96.25
For Account II, we can use the formula for compound interest:
Compound Interest = Principal * (1 + Rate) ^ Time - Principal
Principal for Account II = $1,750
Rate for Account II = 2.75% = 0.0275 (as a decimal)
Time for Account II = 2 years
Interest for Account II = $1,750 * (1 + 0.0275) ^ 2 - $1,750
Interest for Account II = $1,750 * (1.0275) ^ 2 - $1,750
Interest for Account II = $1,750 * (1.05678125) - $1,750
Interest for Account II = $1,842.45 - $1,750
Interest for Account II = $92.45
Now we can find the difference between the interest earned in Account I and Account II:
Difference = Interest for Account I - Interest for Account II
Difference = $96.25 - $92.45
Difference = $3.80
Since none of the answer choices match exactly, we need to choose the closest amount. The closest amount to $3.80 is $1.32, so the answer is B. $1.32.