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3 years ago

D=DVDs and G=Games solve for 2D+3G=15.50 and 3D+1G=12.05

Mathematics

1 answer:

kogti [31]3 years ago

3 0

We have

1G = 12.05 - 3D;

Then,

2D + 3( 12.05 - 3D) = 15.50;

2D + 36.15 - 9D = 15.50;

- 7D = - 20.65;

D = 2.95;

Finally, G = 12.05 - 3 x 2.95;

G = 3.20;

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Using continuous compounding, 6.71 years.

Step-by-step explanation:

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The compound interest formula is given by:

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Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

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In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

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$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

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$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

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$0.07t = \ln{1.6}$

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Using continuous compounding, 6.71 years.

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