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svet-max [94.6K]
3 years ago
10

John is 30 years old. He will receive two payments of $2500 each. The first payment will be an unknown number of years in the fu

ture. The second payment will be five years after the first payment. At an annual effective interest rate of I=5%, the present value of the two payments is $2606. Determine at what age John will receive the second payment.
Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

Answer:

16 years

Step-by-step explanation:

Let us assume that he would received the first payment after t years

So

The following formula should be used

PV = P ÷ (1 + r)^t + P ÷ (1 + r)^t+5

$2,606 = $2,500 ÷ (1 + 0.05)^t + $2,500 ÷ (1 + 0.05)^t + 5

$2,606 = $2,500 ÷ 1.05^t (1 + 1 ÷ (1.05)^5)

1.05^t = $2,500 ÷ $2,606 (1.7835) = 1.71098

t = ln(1.71098) ÷ ln(1.05)

= 11

Therefore he would be received the second payment after

= 11 + 5

= 16 years

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Answer: he invested $46062.5 at 6% and $23031.25 at 10%

Step-by-step explanation:

Let x represent the amount which he invested in the account paying 6% interest.

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The formula for determining simple interest is expressed as

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His annual interest is $7370dollars. it means that

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3 years ago
If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.
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Answer:

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Step-by-step explanation:

Hello,

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So we can say that

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Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

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