Mathematics, 16.01.2020 18:31 josierednour285

Find the time required for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly. round your answer to two decimal places.

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4.14 years required for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Step-by-step explanation:

We are asked to find time it will take for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

We will use compound interest formula to solve our given problem.

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

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years

Upon substituting our given values in above formula, we will get:

$$6800=5000((1+\frac{0.075}{4} )^{4t}\\$

$\frac{6800}{5000} =\frac{5000}{5000} ((1+\frac{0.075}{4}) ^{4t} )$

$1.36=(1+0.01865)^{4t}$

$1.36=(1.01875)^{4t}$

Take natural log of both sides:

$ln(1.36)=ln (1.01875)^{4t}$

ln(1.36)=4t .(1.01875)

$0.3074846997479606=4t. 0.01857638557293\\t=\frac{0.3074846997479606}{4. 0.01857638557293}$

t=4.13811258574

t ≈ 4.14 (up to two decimal places)

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Answer from: jasminebailey829

4.14 years.

Step-by-step explanation:

We are asked to find time it will take for an investment of 5000 dollars to grow to 6800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

We will use compound interest formula to solve our given problem.

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

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years

$7.5\%=\frac{7.5}{100}=0.075$

Upon substituting our given values in above formula, we will get:

$\$6800=\$5000(1+\frac{0.075}{4})^{4*t}$

$\frac{\$6800}{\$5000}=\frac{\$5000(1+\frac{0.075}{4})^{4t}}{\$5000}$

$1.36=(1+0.01875)^{4t}$

$1.36=(1.01875)^{4t}$

Take natural log of both sides:

$\text{ln}(1.36)=\text{ln}((1.01875)^{4t})$

$\text{ln}(1.36)=4t\cdot \text{ln}(1.01875)$

$0.3074846997479606=4t\cdot 0.0185763855729354$

$0.3074846997479606=t\cdot 0.0743055422917416$

$t=\frac{0.3074846997479606}{0.0743055422917416}$

t=4.13811258574

$t\approx 4.14$

Therefore, it will take approximately 4.14 years for an investment of 5000 dollars to grow to 6800 dollars.

Answer from: Quest

the answer is 200

step-by-step explanation:

this is a problem about poisson probabilities. i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.

here's how you can see a poisson distribution coming. when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution. this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot. there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything. the form of the distribution is

probability of n chips = {[e^(-x)]*(x^n)} / (n! )

Answer from: Quest

step-by-step explanation:

jjddbdhid r

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