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Find the interest rate

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Jack invests \$1000 at a certain annual interest rate, and he invests another \$2000 at an annual rate that is one-half percent higher. If he receives a total of \$160 interest in 1 year, at what rate is the \$1000 invested?

Sep 26, 2014

#1
+5

Since 1 percent is 0.01, one-half percent is 0.005.

Let x be the interest rate of the \$1000 investment; then x + 0.005 will be the interest rate of the \$2000 investment.

Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned)

(1000)(x) + (2000)(x+0.005) = 160

1000x + 2000x + 10 = 160

3000x + 10 = 160

3000x = 150

x = 150 / 3000

x = 0.05    ---> The \$1000 is invested at 5%.

Check: (\$1000)(0.05) + (\$2000)(0.055) = \$50 + \$110 = \$160

Sep 26, 2014

#1
+5

Since 1 percent is 0.01, one-half percent is 0.005.

Let x be the interest rate of the \$1000 investment; then x + 0.005 will be the interest rate of the \$2000 investment.

Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned)

(1000)(x) + (2000)(x+0.005) = 160

1000x + 2000x + 10 = 160

3000x + 10 = 160

3000x = 150

x = 150 / 3000

x = 0.05    ---> The \$1000 is invested at 5%.

Check: (\$1000)(0.05) + (\$2000)(0.055) = \$50 + \$110 = \$160

geno3141 Sep 26, 2014