Question

Mauro has $500 to invest in one of two accounts for 3 years.

Account 1 earns 1.2% interest compounded monthly.
Account 2 earns 1.3% interest compounded semiannually.
Which account has a higher return, and how much?
Select the answer that is completely correct.
O Account 2 earns $1.56 more than Account 1.
O Account 1 earns $63.86 more than Account 2.
O Account 2 earns $1.50 more than Account 1.
O Account 1 earns $64.13 more than Account 2.

Answer 1

After calculating the compound interest for both accounts, Account 2, which earns 1.3% interest compounded semiannually, has a higher return than Account 1, which earns 1.2% interest compounded monthly. Account 2 yields $519.56, whereas Account 1 yields $515.69, making the difference between the two $3.87 in favor of Account 2.

Step-by-step explanation:

To determine which investment account provides a higher return after 3 years, we must use the formula for compound interest:

A = P(1 + r/n)nt

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

For Account 1 (compounded monthly):
P = $500
r = 1.2% per year = 0.012
n = 12 (monthly)
t = 3

The equation for Account 1 becomes:
A1 = 500(1 + 0.012/12)12*3

A1 = $515.69 (rounded to two decimal places)

For Account 2 (compounded semiannually):
P = $500
r = 1.3% per year = 0.013
n = 2 (semiannually)
t = 3

The equation for Account 2 becomes:
A2 = 500(1 + 0.013/2)2*3

A2 = $519.56 (rounded to two decimal places)

Now we compare the final amounts:

A2 - A1 = $519.56 - $515.69 = $3.87

Therefore, Account 2 earns $3.87 more than Account 1.