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, and the other has a 4.8% compound 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?
A.
Bank A simple interest account
B.
Bank A compound interest account
C.
Bank B simple interest account
D.
Bank B compound interest account
After leaving the account open for 5 years, Rohan would earn the most interest by choosing Bank A's compound interest account with a 4.8% interest rate. Thus, the answer is B.
To determine which account Rohan should choose in order to earn the most interest after 5 years, we need to compare the interest rates and interest calculation methods offered by each bank.
For Bank A, the simple interest account has a 5% interest rate, and the compound interest account has a 4.8% interest rate.
For Bank B, the simple interest account has a 3% interest rate, and the compound interest account has a 4% interest rate.
To calculate the interest earned in each account after 5 years, we can use the following formulas:
Simple Interest: Interest = Principal * Rate * Time
Compound Interest: A = P(1 + r/n)^(nt) - P
Let's plug in the given information:
Principal (P) = $100.00
Rate (r) for Bank A simple interest account = 5% or 0.05
Rate (r) for Bank A compound interest account = 4.8% or 0.048
Rate (r) for Bank B simple interest account = 3% or 0.03
Rate (r) for Bank B compound interest account = 4% or 0.04
Time (t) = 5 years
For Bank A simple interest account:
Interest = 100 * 0.05 * 5 = $25.00
For Bank A compound interest account:
A = 100 * (1 + 0.048/1)^(1*5) - 100 = $24.88
For Bank B simple interest account:
Interest = 100 * 0.03 * 5 = $15.00
For Bank B compound interest account:
A = 100 * (1 + 0.04/1)^(1*5) - 100 = $21.67
Based on these calculations, Rohan should choose the Bank A simple interest account, as it would earn him the most interest after 5 years. Hence, the correct answer is A. Bank A simple interest account.
To determine which account would earn the most interest for Rohan after 5 years, we need to calculate the interest earned for each option.
For Bank A's simple interest account, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $100, the rate is 5% (or 0.05), and the time is 5 years. So the interest earned would be: Interest = $100 * 0.05 * 5 = $25.
For Bank A's compound interest account, we can use the formula: Future Value = Principal * (1 + Rate/Compounding Periods)^(Compounding Periods * Time). In this case, the principal is $100, the rate is 4.8% (or 0.048), and the compounding periods would depend on the bank's policy. Let's assume it's compounded annually. So the future value would be: Future Value = $100 * (1 + 0.048/1)^(1 * 5) = $121.13.
For Bank B's simple interest account, we can use the same formula as before: Interest = Principal * Rate * Time. In this case, the principal is $100, the rate is 3% (or 0.03), and the time is 5 years. So the interest earned would be: Interest = $100 * 0.03 * 5 = $15.
For Bank B's compound interest account, let's apply the same assumptions as before. Using the formula: Future Value = Principal * (1 + Rate/Compounding Periods)^(Compounding Periods * Time), the future value would be: Future Value = $100 * (1 + 0.04/1)^(1 * 5) = $121.67.
After analyzing the calculations, we can see that the Bank A compound interest account would earn Rohan the most interest after leaving the account open for 5 years (with a future value of $121.13). Therefore, the correct answer is B. Bank A compound interest account.