Question

A bank offers two different types of interest on savings accounts.

Account I pays 5.5% simple interest.
Account II pays 5% interest compounded annually.
Deposits of $1,000 are made into the accounts. Which account would be the better choice deposit $1,000 in for 5 years?

Answer 1

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