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Samantha invests a total of $21,500 in two accounts paying 12% and 15% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,685.00what was invested at %12 and %15

User David Berger
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18 votes
Answer:

$18000 was invested at 12%

$3500 was invested at 15%

Explanations:

Let the amount invested in the first account be P₁

Let the amount invested in the scond account be P₂

A total of $21500 was invested in the two accounts

That is:

P₁ + P₂ = 21500................(1)

Interest = Principal x Rate x Time

Time = 1 year

Rate charged on the first account, R₁ = 12% = 12/100 = 0.12

Rate charged on the second account, R₂ = 15% = 15/100 = 0.15

Interest on first account = P₁ x R₁ x T

Interest on first account = P₁ x 0.12 x 1 = 0.12P₁

Interest on second account = P₂ x R₂ x T

Interest on second account = P₂ x 0.15 x 1 = 0.15P₂

The total interest charged is $2685

(Interest on first account) + (Interest on second account) = Total interest

0.12P₁ + 0.15P₂ = 2685.................................(2)

Make P₁ the subject of the formula from equation (1)

P₁ = 21500 - P₂...............................(3)

Sustitute equation (3) into equation (2)

0.12 ( 21500 - P₂) + 0.15P₂ = 2685

2580 - 0.12P₂ + 0.15P₂ = 2685

0.03P₂ = 2685 - 2580

0.03P₂ = 105

P₂ = 105/0.03

P₂ = 3500

Substitute the value of P₂ into equation (3)

P₁ = 21500 - 3500

P₁ = 18000

$18000 was invested at 12%

$3500 was invested at 15%

User Newtt
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