Question

Three different accounts are described below. Order the accounts according to their values after 10 years, from greatest to least.

You deposit $950 in an account that earns 5% interest semiannually.
You deposit $800 in an account that earns 7.5% annual interest compounded quarterly.
You deposit $700 in an account that earns 7.75% annual interest compounded monthly.

Answer 1

• $800 at 7.5%
• $950 at 5%
• $700 at 7.75%

Explanation:

You want to order the accounts greatest to least by their value after 10 years.

• $950 at 5%, compounded semiannually
• $800 at 7.5%, compounded quarterly
• $700 at 7.75%, compounded monthly

Value

The value of each account can be found using the compound interest formula:

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

Principal P earning rate r compounded n times per year for t years.

For the three accounts, the corresponding values are ...

• 950(1 +0.05/2)^(2·10) = 1556.69
• 800(1 +0.075/4)^(4·10) = 1681.88 . . . . . . . greatest value
• 700(1 +0.0775/12)^(12·10) = 1515.63 . . . . . least value

Comparison

The order, greatest to least, according to the account values is ...

• $800 at 7.5%
• $950 at 5%
• $700 at 7.75%

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Additional comment

The $700 account will overtake the $950 account after 11 years. It will take about 46 years for it to overtake the $800 account. Eventually, the higher interest rate with greater frequency of compounding wins out.

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