A person invested
$
8
,
900
$8,900 in an account growing at a rate allowing the money to double every 7 years. How long, to the nearest tenth of a year would it take for the value of the account to reach
$
20
,
600
$20,600?
Answers
Answer:
8.5
Explanation:
To the nearest tenth of a year, it would take around 9.1 years when calculate compoundly for the account's worth to reach $20,600.
What is Compound interest?A loan or investment's initial principal as well as any accrued interest from earlier periods are both taken into account when calculating compound interest.
To resolve this issue, we can apply the compound interest formula:
A = P(1 + r/n)nt
where:
A represents the balance of the account after t years.P stands for the initial outlay ($8,900 in this case).The annual interest rate is r, which is unknown.The number n determines how often interest is compounded each year (in this case, once every seven years because the value of the money doubles every seven years).The number of years is t.When A = $20,600, we need to determine t. Since we are aware that the initial investment would double after seven years, we can use the following formula to determine the yearly interest rate:
2 = (1 + r/n)^(nt)
If n is 1/7 (since the investment twice once every 7 years), 2 is the factor by which the investment doubles, and t is an unknown.
When we simplify this equation, we obtain:
t log(1 + r/7) = log(2)
When we solve for r, we get:
r = 7[(2^(1/t))-1]
Now that we have P, r, n, and A, we can enter them into the compound interest formula to find t:
$20,600 = $8,900(1 + r/1)^(1t)
2.318 = (1 + r)^t = log (2.318) / log (one plus r)
t is equal to log(2.318)/log(1 + 7[(2(1/t))-1]).
We can iteratively solve for t using a calculator, beginning with a first guess of 7 years (because the investment doubles every 7 years):
r = 0.0998 and A = $17,800 for t = 7 years
r = 0.0909 and A = $19,397 for t = 8 years.
r = 0.0833 and A = $20,416 for t = 9 years.
r = 0.0823 and A = $20,601 (closest to $20,600) for t = 9.1 years
As a result, it would take the account's value to reach $20,600 in around 9.1 years (to the nearest tenth of a year).
Therefore, when calculated compoundly, it would take approximately 9.1 years for the account's value to reach $20,600, to the nearest tenth of a year.
Learn more about Compound interest, here:
https://brainly.com/question/18958915
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Answer:
La distancia horizontal que recorrerá la caja con medicina antes de caer al río es 583.1 metros.
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En este caso, reemplazando los datos conocidos, teniendo en cuenta que el MRUV sucede en la trayectoria vertical y que la aceleración es el valor de la gravedad:
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Posición final= 583.1 m
La distancia horizontal que recorrerá la caja con medicina antes de caer al río es 583.1 metros.
Veremos que la distancia horizontal que recorre la caja es 583.1 metros.
¿Como encontrar la distanca horizontal recorrida?Recordar que la velocidad vertical y horizontal son independientes.
Aqui, lo primero que debemos hacer es encontrar el tiempo que la caja tarda en llegar al suelo.
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La caja llegara al suelo cuando la función de arriba sea igual a cero:
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