Rohan has $100.00 that he wants to save in a bank. Bank A offers two types of savings accounts. One has a 5% simple interest rate. Bank B also offers two types of savings accounts. One has a 3% simple interest rate, and the other has a 4% compound interest rate.
Use the passage to answer the question.
Which account should Rohan choose in order to earn the most interest after leaving the account open for 5 years?
(1 point)
A. Bank A simple interest account
B. Bank A compound interest account
C. Bank B simple interest account
D. Bank B compound interest account
To determine which account will earn the most interest after 5 years, we need to calculate the interest earned for each option.
Option A: Bank A simple interest account with a 5% interest rate
The formula for simple interest is: I = P * r * t, where I is the interest earned, P is the principal (initial amount), r is the interest rate, and t is the time in years.
Substituting the values, we get: I = $100 * 0.05 * 5 = $25
Option B: Bank A compound interest account with a 4% interest rate
The compound interest formula is: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the values, we get: A = $100(1 + 0.04/1)^(1*5) ≈ $121.67
Option C: Bank B simple interest account with a 3% interest rate
Using the same formula as in option A, we get: I = $100 * 0.03 * 5 = $15
Option D: Bank B compound interest account with a 4% interest rate
Using the same formula as in option B, we get: A = $100(1 + 0.04/1)^(1*5) ≈ $121.67
Comparing the results:
Option A: $25
Option B: $121.67
Option C: $15
Option D: $121.67
Based on the calculations, the option that will earn the most interest after 5 years is option B: Bank A compound interest account.