Answer:
After 5 years, Account II (compounded interest) yields a slightly higher balance than Account I (simple interest). Therefore, for a $1,000 deposit over 5 years, Account II would be the better choice as it provides a slightly higher return due to compounding.
Explanation:
To determine which account is the better choice, we can calculate the final balance for both Account I (simple interest) and Account II (compounded interest) after 5 years.
Account I (Simple Interest):
Principal (P) = $1,000
Rate (R) = 5.5% = 0.055 (in decimal form)
Time (t) = 5 years
Simple Interest formula:
Simple Interest (SI) = P * R * t
SI = $1,000 * 0.055 * 5 = $275
Total Balance = Principal + Simple Interest
Total Balance = $1,000 + $275 = $1,275
Account II (Compound Interest):
Principal (P) = $1,000
Rate (R) = 5% = 0.05 (in decimal form)
Time (t) = 5 years
Frequency of compounding (n) = 1 (annually)
Compound Interest formula:
Total Balance = P * (1 + R/n)^(n*t)
Total Balance = $1,000 * (1 + 0.05/1)^(1*5)
Total Balance = $1,000 * (1.05)^5 ≈ $1,276.28
Comparing the balances:
Account I (Simple Interest): $1,275
Account II (Compound Interest): $1,276.28