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umka21 [38]
3 years ago
14

$9500 is invested part of it at 12% and part of it at 9%, for a certain year the total yield is $1032.00. How much was invest at

each rate?
Mathematics
1 answer:
svet-max [94.6K]3 years ago
8 0

so what i did was a long process but it worked i started by taking $5550 and multiplying it by .12 which gave me $666 then i did 9500-5550=3950 then i took 3950 and multiplied it by .09 and it gave me 355.5 then i added those together and got 1021.5 so i needed to increase the amount i invested at 12% to get a higher yield. i did this process a few more times and each time i increase the amount of money i invested at 12% by 25 dollars and i finally arrived at:

5900 x .12 = $708

9500-5900=3600

3600 x .09 =$324

708+324= $1032

so your answer is that you invested $5900 at 12% and $3600 at 9%.

add me as a friend if you like because i am generally good at math. hope this helped.

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Answer:

The compounded annually account will earn more interest over 10 years

Step-by-step explanation:

The rule of the simple interest is I = Prt, where

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The rule of the compounded interest is A = P(1+\frac{r}{n})^{nt}, where

  • A is the new value
  • P is the original value
  • r is the rate in decimal
  • n is the number of periods
  • t is the time

The interest I = A - P

∵ Each account start with $200

∴ P = 200

∵ They have an interest rate of 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ One account earns simple interest and the other is compounded  

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∴ n = 1 ⇒ compounded annually

∵ The time is 10 years

∴ t = 10

→ Substitute these values in the two rules above

∵ I = 200(0.05)(10)

∴ I = 100

∴ The simple interest = $100

∵ I = A - P

∵ A = 200(1+\frac{0.05}{1})^{1(10)}

∴ A = 325.7789254

∵ I = 325.7789254 - 200

∴ I = 125.7789254

∴ The compounded interest = $125.7789254

∵ The simple interest is $100

∵ The compounded interest is $125.7789254

∵ $125.7789254 > $100

∴ The compounded annually account will earn more interest

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