Question

7. A total of $12,000 was invested in two types of bonds. One pays 8% simple interest while the other
pays 10.5%. Last year, the annual interest earned on the two investments was $1,145. How much was
invested at each rate?

Answer 1

Answer:

Step-by-step explanation:

Let x = $ invested in 8% account

y= $ invested in 10.5% account

x + y= 12000

0.08x + 0.105y = 1145

$4600 invested in the 8% account

and $7400 invested in the 10.5%

account

Answer 2

The amount invested at each rate is :

• At 8% = 4600
• At 10.5% = 7400

Total interest earned = $1145

Total principal = 12000

Recall :

Simple interest = Principal × Rate × time

Let amount invested in A = p

Investment A :

Principal = p

Rate = 8%

time = 1

Interest earned = (p × 0.08 × 1) = 0.08p - - - (1)

Investment B :

Principal = 12000 - p

Rate = 10.5%

time = 1

Interest earned = (12000 - p × 0.105 × 1) = 1260 - 0.105p - -(2)

Summing the interest earned, we should obtain $1145

0.08p + (1260 - 0.105p) = 1145

0.08p + 1260 - 0.105p = 1145

-0.025p = 1145 - 1260

-0.025p = - 115

p = 115 ÷ 0.025

p = 4600

At 8%:

p = 4600

At 10.5%:

12000 - p = 12000 - 4600 = 7400

Hence, the amount invested at each amount is 4600 and 7400

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