Question

Zhong has money to invest in one of two accounts for 2

years.

Account 1 requires a $1,200
investment and earns 2.7%
interest compounded daily.
Account 2 requires a $1,000
investment and earns 3.9%
interest compounded annually.

Which account has a higher return?

Answer 1

To compare the returns from two investment accounts with different compound interest rates and frequencies, one must calculate the final balances using the formula for compound interest and then compare them.

Step-by-step explanation:

To determine which account has a higher return after 2 years, we need to calculate the final balance of each account using the formula for compound interest:

A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

For Account 1:

P = $1,200, r = 2.7% or 0.027, n = 365 (daily), t = 2 years.

Final balance for Account 1: A1 = 1200(1 + 0.027/365)^(365*2)

For Account 2:

P = $1,000, r = 3.9% or 0.039, n = 1 (annually), t = 2 years.

Final balance for Account 2: A2 = 1000(1 + 0.039/1)^(1*2)

We must calculate these values to determine which account offers a higher return after 2 years.