You win $10 000 in a Best Math Student competition. Being a generous person, you decide to invest the money


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 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?

Respuesta :

Cumulative costs of the investments of a mutual fund you currently hold are the amount invested. Net Investment is one investment action's net amount of inflow.

  • Invested Amount in PP [tex]\bold{= \$2400}[/tex]
  • Invested Amount in TT [tex]\bold{= \$(10000 - 2400) = \$7600}[/tex]

Solution:

The formula for calculating the simple interest:  

[tex]\to \text{Simple interest} = principal \times rate \times time[/tex]

Total amount = 10000

Let :

  • Invested Principle (PP) [tex]\bold{= r}[/tex]  ............................. (i)
  • Invested Amount in TT [tex]\bold{= 10000 - r}[/tex]     ................................. (ii)

From both investments total earned interest  = $620

[tex]\to \bold{PP \ investment \ return + TT \ investment\ return = 620}[/tex]

[tex]\to (r \times 10\% \times 1) + (10000 - r \times 5\% \times 1) = 620\\\\\to (r \times \frac{10}{100} \times 1) + (10000 - r \times \frac{5}{100} \times 1) = 620\\\\\to (r \times 0.10 \times 1) + (10000 - r \times 0.05 \times 1) = 620\\\\\to 0.1r + 500 - 0.05r = 620\\\\\to 0.05r = 620 - 500\\\\\to 0.05r = 120\\\\\to r =\frac{ 120}{0.05}\\\\\to r = 2400[/tex]

Therefore,

  • Invested Amount in PP [tex]\bold{= \$2400}[/tex]
  • Invested Amount in TT [tex]\bold{= \$(10000 - 2400) = \$7600}[/tex]

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