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Last year, Henry had $30,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 5% simple interest per year. After one year, he received a total of $1760 in interest. How much did he invest in each account? First account: Second account:

Respuesta :

Solution

Step 1

Total amount invested = $30,000

Step 2:

First account

Money invested = m

interest rate = 7%

Time = 1 year

Interest = ?

Second account

Money invested = 30000 - m

interest rate = 5%

Time = 1 year

Interest = ?

Step 3:

Interest received from the first investment

[tex]\begin{gathered} Interest\text{ = }\frac{PRT}{100}\text{ = }\frac{m\times7\times1}{100}\text{ = 0.07m} \\ \end{gathered}[/tex]

Interest received from the second investment

[tex]Interest\text{ = }\frac{PRT}{100}\text{ = }\frac{\lparen30000-m\rparen\times5\times1}{100}\text{ = 0.05\lparen30000 - m\rparen}[/tex]

Step 4:

Total interest = $1760

[tex]\begin{gathered} \text{0.07m + 0.05\lparen30000 - m\rparen = 1760} \\ 0.07m\text{ + 1500 - 0.05m = 1760} \\ 0.02m\text{ = 1760 + 1500} \\ 0.02m\text{ = 260} \\ \text{m = }\frac{260}{0.02} \\ \text{m = \$13000} \end{gathered}[/tex]

Final answer

How much did he invest in each account?



First account: $13000



Second account: ​$17000