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fiasKO [112]
3 years ago
15

Monica deposited $26000 in an account that pays 4% interest compounded annually. How much money does she earn after 10 years?

Mathematics
1 answer:
enyata [817]3 years ago
5 0
Heres the formula for compound interest:
A=P(1+\frac{r}{n})^nt
A is the amount over 10 years
P is the initial deposit ($26,000)
r is the annual interest rate (4% or .04)
n is the number of times that interest is compounded annually (1)
t is the number of years the money is invested (10 yrs)
A=26000(1+\frac{.04}{1})^(1)(10)
A=26000(1.04)^10
A=26000(<span>1.48024428492)
A=$</span><span>38,486.3514079
(Simplified she would have $38,486.35)
</span>
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Given this information, we can conclude that 74% of the cars won't need any repairs over a 1-year period (100 - 20 - 5 - 1 = 74%). And 26% will need at least 1 repair over a 1-year period.

P(car doesn't need repair) = 0.74

P (car needs repair) = 0.26

If you own two cars, the probability that:

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We need that car 1 won't need repair AND car 2 won't need repair.

=P(Car 1 doesn't need repair) x P(Car 2 doesn't need repair)

= 0.74 x 0.74 = 0.5476

The probability that neither will need repair is 0.5476.

<u>b) Both will need repair:</u>

We need that car 1 needs repair AND car 2 needs repair.

P(Car 1 needs repair) x P(Car 2 needs repair)

= 0.26 x 0.26 = 0.0676

The probability that both will need repair is 0.0676

<u>c) At least one car will need repair</u>

Car 1 needs repair or Car 2 needs repair or both need repair.

To solve this one, it's easier to use the complement of P(neither needs repair)

1 - P(neither needs repair)

1 - (0.74)(0.74)  = 1 - 0.5476 = 0.4524

The probability that at least one car will need repair is 0.4524

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