Last year, Tammy had $20,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1060 in interest. How much did she invest in each account?

Question

09-10-2017
Mathematics

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Last year, Tammy had $20,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1060 in interest. How much did she invest in each account?

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jdoe0001 jdoe0001 · Answer 1 · 2017-10-09T20:44:28+02:00

is pretty much the same as the Pablo buying the computers and City charges, so without much fuss let's proceed.

a = invested at 7%

b = invested at 5%

we know she invested a total of 20,000, thus a + b = 2000.

how much is 7% of a? (7/100) * a, 0.07a.

how much is 5% of b? (5/100) * b, or 0.05b

we know the yield is 1060, thus 0.07a + 0.05b = 1060.

[tex]\bf \begin{cases} a+b=20000\implies \boxed{b}=20000-a\\ 0.07a+0.05b=1060\\ ----------\\ 0.07a+0.05\left( \boxed{20000-a} \right)=1060 \end{cases} \\\\\\ 0.07a+1000-0.05a=1060\implies 0.02a=60 \\\\\\ a=\cfrac{60}{0.02}\implies a=3000[/tex]

how much was invested at 5%? well, b = 20000 - a.