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Sedbober [7]
3 years ago
11

Paul has $30000 to invest. His intent is to earn 10% interest on his investment. He can invest part of his money at 6% interest

and part at 13% interest. How much does Paul need to invest in each option to make get a total 10% return on his $30000?
Investing for 6% return: $
.
Investing for 13% return: $

Thanks a ton! :)
Mathematics
1 answer:
MrRa [10]3 years ago
5 0

Answer:

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Step-by-step explanation:

Let

x ----> the amount invested at 6%

30,000-x -----> the amount invested at 13%

we know that

The interest earned by the amount invested at 6% plus the interest earned by the amount at 13% must be equal to the interest earned by the total amount of $30,000 at 10%

Remember that

6\%=6\100=0.06

13\%=13\100=0.13

10\%=10\100=0.10

so

The linear equation that represent this situation is

0.06x+(30,000-x)0.13=0.10(30,000)

solve for x

0.06x+3,900-0.13x=3,000\\0.13x-0.06x=3,900-3,000\\0.07x=900\\x=\$12,857.14$

x-\$30,000=\$17,142.86

therefore

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

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Answer:

Question 5

a)Simple Interest = Nu 450, Total Amount = Nu 6,450

b)Simple Interest = Nu 250, Total Amount = Nu 12,750

c)Simple Interest = Nu 2,880, Total Amount = Nu 10,880

Question 6

The amount of commission Mindu earned was Nu 4,750

Step-by-step explanation:

Question 5

Simply Interest formula is given as

I = P × R × T

Total Amount = P + I

Where

P = Principal

R = Rate

T = Time in years

I = Interest

a) P = Principal = Nu 6000

R = Rate = 15% = 0.15

T = Time = 6 months , converting to years = 6/12 months = 0.5years

I = Interest = 6000 × 0.15 × 0.5

I = Nu 450

Amount = P + I

= Nu 6000 + Nu 450

= Nu 6,450

Simple Interest = Nu 450, Total Amount =Nu 6,450

b) P = Principal = Nu 12,500

R = Rate = 8% = 0.08

T = Time = 3 months , converting to years = 3/12 months = 0.25 years

I = Interest = 12,500 × 0.08 × 0.25

I = Nu 250

Amount = P + I

= Nu 12,250 + Nu 240

= Nu 12,750

Simple Interest = Nu 250, Total Amount =Nu 12,750

c) P = Principal = Nu 8000

R = Rate = 12% = 0.12

T = Time = 3years

I = Interest = 6000 × 0.12 × 3

I = Nu 2,880

Amount = P + I

= Nu 8000 + Nu 2,880

= Nu 10,880

Simple Interest = Nu 2,880, Total Amount = Nu 10,880

Question 6

We are told in the question that each month:

If sales are up to Nu 75,000, = Mindu earns 3% commission

If sales are over Nu 75,000 = Mindu earns 5% commission

Last month, Mindu has sales of Nu 95,000

Since his sales was above Nu 75,000 he earns a 5% commission

Therefore, the amount he earned as commission is calculated as:

Nu 95,000 × 5%

= Nu 4,750

Therefore, the amount of commission Mindu earned was Nu 4,750

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