Question

1. nadia deposits $2,250 into each of two savings accounts.

• account i earns 1.25% annual simple interest.
• account ii earns 1.25% interest compounded annually.

nadia does not make any additional deposits or withdrawals. which amount is closest to the difference between the interest nadia will earn in account i and the interest nadia will earn in account ii at the end of 2 years?
options: $56.25, $0.35, $56.60, $112.85

Explanation:

Step1: Calculate Simple Interest for Account I

The formula for simple interest is \( I = P \times r \times t \), where \( P = 2250 \), \( r = 0.0125 \), \( t = 2 \).
\( I_1 = 2250 \times 0.0125 \times 2 = 2250 \times 0.025 = 56.25 \).

Step2: Calculate Compound Interest for Account II

The formula for compound interest is \( A = P(1 + r)^t \), so interest \( I_2 = A - P \).
\( A = 2250(1 + 0.0125)^2 = 2250(1.0125)^2 \approx 2250 \times 1.02515625 \approx 2306.59 \).
\( I_2 \approx 2306.59 - 2250 = 56.59 \).

Step3: Find the Difference

Difference \( = |I_2 - I_1| \approx |56.59 - 56.25| = 0.34 \approx 0.35 \).

Answer:

$0.35$