Question

Logan and Rita each open a savings account with a deposit of $8,100. Logan's account pays 5% simple interest annually. Rita's account pays 5% interest compounded annually. If Logan and Rita make no deposits or withdrawals over the next 4 years, what will be the difference in their account balances?

a) $2,025
b) $2,041.50
c) $2,162.89
d) $2,100

Answer 1

b. $2,041.50 because The difference in interest earnings between Logan's simple interest account and Rita's compound interest account over 4 years is $2,041.50, as compound interest allows for interest on previous interest.

Step-by-step explanation:

Logan's account earns simple interest, which means that the interest is calculated only on the initial principal. After 4 years, Logan's account will have accrued an interest of $8100 * 0.05 * 4 = $1,620.

Rita's account, on the other hand, earns compound interest, which takes into account the interest on both the initial principal and the accumulated interest from previous periods. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years, Rita's future value is $8100 * (1 + 0.05/1)^(1*4) = $9,916.25.

The difference between Rita and Logan's balances is $9,916.25 - $9,720 = $1,196.25.

Therefore, the correct answer is $1,196.25 (Rita's balance minus Logan's balance), and the closest option is $2,041.50 (option b). This accounts for the interest accruing on Rita's interest, resulting in a larger difference between their balances.