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koban [17]
3 years ago
10

Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawa

ls are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?
Mathematics
1 answer:
Vaselesa [24]3 years ago
6 0

Answer:

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

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Step-by-step explanation:

Simple interest formula

A = P (1 + rt)

Compound interest formula

A = P(1 + \frac{r}{n})^{nt}

a.

A = 5000 (1 + 0.025*1)\\A=5000(1.025)\\A=5125

Simple interest is $125

b

. A = 5000 (1 + \frac{0.025}{1})^{1*1}      \\A=5000(1.025)\\A= 5125

Compound interest is $125

c. the result for both a and b are the same

d.

A = 5000 (1 + 0.025*3) \\A=5000(1.075) \\A=5375

the simple interest is $375

e

. A = 5000 (1 + \frac{0.025}{1})^{1*3}] \\A=5000(1.025)^3 \\A=5000(1.077)\\A= 5385

the compound interest is $385

f. the result compared, compound interest is $10 more than simple interest

g.

A = 5000 (1 + 0.02*6) \\A=5000(1.12) \\A=5600

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h.

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i. the result from g and h, h is over 8 times bigger than g.

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Answer:

g (15) represents the radius (in cm) of a circle whose circumference is 15 cm

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Step-by-step explanation:

In a circle the following relationship can be posed:

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Let g be a function that determines the radius of the circle from the value of its circumference, so, you have:

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Thus, g (15) represents the radius (in cm) of a circle whose circumference is 15 cm. You have to g (15) =\frac{15}{2\pi}.

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