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Elis [28]
3 years ago
13

Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight

-year life. What would be the present value of this loan if it carried a 10% interest rate?
Mathematics
1 answer:
lapo4ka [179]3 years ago
3 0

Answer:

The present value is  PV  = \$ 396,987

Step-by-step explanation:

From the question we are told that

   The  interest payment per year is  C =  \$ 85

    The principal payment is  P =  \$ 1000

     The  duration is  n =  8   years

      The  interest rate is  r =  10\%  =  0.10

The present value is  mathematically represented as

      PV  =  [ \frac{C}{r} *  [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n}  ]

substituting values

      PV  =  [ \frac{85}{0.10} *  [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8}  ]

      PV  = \$ 396,987

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8 0
3 years ago
The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 18, meaning that among
jeyben [28]

Answer:

(a) The value of P (None) is 0.062.

(b) The value of P(at least one) is 0.938.

(c) The value of P(at most one) is 0.253.

(d) The event is not unusual.

Step-by-step explanation:

Let <em>X</em> = number of households watching the show.

The probability of the random variable <em>x</em> is, P (X) = <em>p</em> = 0.18.

The sample selected for the survey is of size, <em>n</em> = 14

The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 14 and <em>p</em> = 0.18.

The probability of a Binomial distribution is computed using the formula:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...

(a)

Compute the probability that none of the households are tuned to CSI: Shoboygan as follows:

P(X=0)={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}=1\times1\times0.06214=0.062

Thus, the value of P (None) is 0.062.

(b)

Compute the probability that at least one household is tuned to CSI: Shoboygan as follows:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

             =1-0.062\\=0.938

Thus, the value of P(at least one) is 0.938.

(c)

Compute the probability that at most one household is tuned to CSI: Shoboygan as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

             ={14\choose 0}(0.18)^{0}(1-0.18)^{14-0}+{14\choose 1}(0.18)^{1}(1-0.18)^{14-1}\\=0.062+0.191\\=0.253

Thus, the value of P(at most one) is 0.253.

(d)

An event that has a very low probability of occurrence is known as an unusual event.

The probability of the event "at most one household is tuned to CSI: Shoboygan" is 0.253.

This probability value is not low.

Hence, the event is not unusual.

5 0
3 years ago
The volume of a cylinder is 2,200 pie cubic inches. The diameter of the circular base is 10 inches. What is the height of the cy
Elis [28]

Answer:

Step-by-step explanation:

H = V/ pie r^2

H = \frac{2200pie}{Pie 5^2}

R= 5 because the radius is half the diameter

Pies cancel out leaving you with:

H = 2200/5^2

H = 2200/25

H = 88

Hope this helps :)

5 0
3 years ago
The total cost after tax to repair Deborah's computer is represented by0.08(50h)+50H, where h is the number of hours it takes to
katrin2010 [14]

Answer:

.08(50h) Because if the tax rate is 8%, then that is 1.08% of 50h.

Step-by-step explanation:

5 0
3 years ago
The pie chart shows information about voters in an election. 3360
Lesechka [4]

Answer:

4838 total number of voters

Step-by-step explanation:

In a whole circle there 360°, in a straight line theres 180°.

180-110=70 first to break it down to find the degrees of women.

180+70=250° for women.

250°=3360

we need to find 110° of men

25°=336

times 4

100°=1344

divide by 10

10°=134.4 round down 134

1344+134=1478

3360+1478=4838

7 0
2 years ago
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