Respuesta :
Simple interest is a method of calculating interest on an amount. The sum of the total balances of these accounts at the end of 7 years is $27,822.54.
What is simple interest?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
[tex]\rm Simple\ Interest=\dfrac{P\times R \times T}{100}[/tex]
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
As it is given that the amount deposited by James is $12,000. While the interest earned on the first account is 2.2% compounded annually for a period of 7 years, therefore, the balance in the account will be,
[tex]\text{Account balance of first Account} = P(1+r)^t = 12,000(1.022)^7=\$13,974.54[/tex]
In the second account, James deposited $12,000 at a rate of 2.2% annual simple interest. Therefore, the balance in the account will be,
[tex]\text{Account balance of second Account} = P+\dfrac{P\times R \times T}{100}[/tex]
[tex]=12,000+\dfrac{12,000 \times 2.2 \times 7}{100} \\\\= \$13,848[/tex]
Now, the balance of the account when combined together will be,
[tex]\rm Total\ Balance = \text{Account balance of first Account} +\text{Account balance of second Account} \\\\\rm Total\ Balance = \$13,974.54+\$13,848 = \$27,822.54[/tex]
Hence, the sum of the total balances of these accounts at the end of 7 years is $27,822.54.
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