Suki invested $20,000, some at 5% interest and the rest at 10%. How much did she invest at each rate if she received $1,400 in interest in one year?

Question

Mathematics

Kristopher

15 December, 15:12

Suki invested $20,000, some at 5% interest and the rest at 10%. How much did she invest at each rate if she received $1,400 in interest in one year?

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Petersen · Answer 1

Suki invested $12,000 at 5% and $8,000 at 10%

Step-by-step explanation:

Step 1: Principal = $20,000, Interest 1 Rate, R1 = 5% and Interest 2 Rate, R2 = 10%, Time = 1 year and total interest = $1400

Let the amount invested at R1 be P1 and that invested at R2 be 20000 - P1

⇒ Total Interest = P1*R1*T/100 + (20000 - P1) * R2*T/100 (since Simple Interest = PRT/100)

⇒ Total Interest = T/100 [P1R1 + (20000 - P1) R2] (Taking out the common factors)

⇒ 1400 = 1/100 (5P1 + 20,000 * 10 - 10P1)

⇒ 140,000 = - 5P1 + 200,000

⇒ 5P1 = 60,000

⇒ P1 = 60,000/5 = $12,000

⇒ P2 = 20,000 - P1 = $8,000