Question

You win $10 000 in a Best Math Student competition. Being a generous person, you decide to invest the money in two local businesses to help them get off the ground. The businesses are Paul’s Paper and Tiffany’s Tyres. They offer the following annual interest rates return to encourage your investment;
PP – 10% p.a.

TT – 5% p.a.

The investment's combined return is $620 after one year. How much was invested in each company?

Answer 1

The amount invested in each company is :

• Amount invested in PP = $2400
• Amount invested in TT = $(10000 - 2400) = $7600

Using the simple interest relation:

Simple interest = principal × rate × time

Total amount = 10000

Let :

principal invested in PP = r

HENCE, amount invested in TT = 10000 - r

Total interest earned on both investments = $620

PP investment return + TT investment return = 620

(r × 10% × 1) + (10000 - r × 5% × 1) = 620

0.1r + 500 - 0.05r = 620

0.05r = 620 - 500

0.05r = 120

r = 120 / 0.05

r = 2400

Hence,

Amount invested in PP = $2400

Amount invested in TT = $(10000 - 2400) = $7600

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