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olganol [36]
3 years ago
8

Margaret deposits $1,000 in a savings account that pays 1.4% interest compounded

Mathematics
1 answer:
ozzi3 years ago
8 0

Answer:

The balance after 1 year is;

$1,014.05

Step-by-step explanation:

To do this, we use the compound interest formula

That will be ;

A =P (1 + r/n)^nt

A is the amount generated which we want to calculate

r is the rate = 1.4% = 0.014

P is the amount deposited = $1,000

n is the number of times it is compounded annually which is 2 (semi-annually means 2 times in a year)

this the number of years which is 1

we have this as:

A = 1,000( 1 + 0.014/2)^(2*1)

A = 1,000(1 + 0.007)^2

A = 1,000(1.007)^2

A = $1,014.05

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3) Para maximizar su beneficio diario el director debería cobrar cada habitación a €56.

4) El fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.

3- Dado que las 80 habitaciones de un motel se podrían alquilar todas las noches si el director cobrara 40€ o menos por habitación, y si se cobra (40+x) € por habitación, entonces 2x habitaciones permanecerán vacantes, para determinar, si cada habitación alquilada le cuesta al director 10 € al día y cada habitación no alquilada 2 € al día, qué precio debería cobrar el director por habitación para maximizar su beneficio diario, se deben realizar los siguientes cálculos:

  • 80 x 40 - 80 x 2 = 3040
  • 70 x 50 - 10 x 10 - 70 x 2 = 3260
  • 60 x 60 - 20 x 10 - 60 x 2 = 3280
  • 65 x 55 - 15 x 10 - 65 x 2 = 3295
  • 66 x 54 - 14 x 10 - 66 x 2 = 3292
  • 64 x 56 - 16 x 10 - 64 x 2 = 3296
  • 63 x 57 - 17 x 10 - 63 x 2 = 3295

Por lo tanto, para maximizar su beneficio diario el director debería cobrar cada habitación a €56.

3) Dado que un fabricante de automóviles vende 2000 coches al mes, con un beneficio medio de 1000 € por coche, y las prospectivas de mercado indican que por cada 50 € de descuento que el fabricante ofrezca a los compradores podría vender 200 coches más al mes, para determinar cuánto descuento debería ofrecer para maximizar el beneficio mensual se debe realizar el siguiente cálculo:

  • 1000 x 2000 = 2.000.000
  • 900 x 2400 = 2.160.000
  • 800 x 2800 = 2.240.000
  • 700 x 3200 = 2.240.000
  • 600 x 3600 = 2.160.000
  • 850 x 3000 = 2.550.000

Por lo tanto, el fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.

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