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Nadusha1986 [10]
3 years ago
12

​(Annuity payments) Calvin Johnson has a 5000 debt balance on his Visa card that charges 12.9 percent APR compounded monthly. In

2009 , Calvin's minimum monthly payment is 3 percent of his debt​ balance, which is $150. ​How many months​ (round up) will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $150 at the end of each month?
Business
2 answers:
olya-2409 [2.1K]3 years ago
8 0

Answer:

41.49 approx 42 months

Explanation:

To calculate the number of months, we use the formula for loan

p = r(pv) / 1 - (1+r)-n

make n subject of the formula

p ( 1 - ( 1+r) ^-n) = r(pv)

p - p (1+r)^-n = r(pv)

p (1+r)^-n = p-r(pv)

(1+r)^-n = (p-r(pv)) / p

( 1+r)^n = p / (p-r(pv))

n In( 1+r) = In (p / (p-r(pv))

n = In ( p/ ( p - r(pv)) / In ( 1 +r)

n is the number of months, p is the payment per months

pv is the present value of 5000

substitute the values given into the equation

n = (In ( 150 / (150 - ( 0.129 / 12 × 5000)) / ( In ( 1 + ( 0.129 / 12) = 41.49 approx 42 months

STatiana [176]3 years ago
8 0

Answer:

42 months

Explanation:

To calculate the number months, we use ordinary annuity formula since that payment is expected to be made at the end of each month. The ordinary annuity formula is as follows:

PV = P × [{1 - [1 ÷ (1 + r)]^n} ÷ r]  .............................. (1)

Where ,

PV = Present value of an annuity  payment = $5,000

P = monthly payment  = $150

r = interest rate  = 12.9% annually = 0.129 annually = (0.129 ÷ 12) monthly =  0.01075  monthly

n = number of months = ?

Substituting the values into equation (1), we have:

5000 = 150 × [{1 - [1 ÷ (1 + 0.01075)]^n} ÷ 0.01075]  

5000 ÷ 150 = {1 - [1 ÷ (1.01075)]^n} ÷ 0.01075

33.33 × 0.01075 = 1 - [1 ÷ (1.01075)]^n

1 - 0.36 = [1 ÷ (1.01075)]^n

0.64 = 1^n ÷ (1.01075)^n

Since 1^n = 1, we have:

0.64 = 1 ÷ (1.01075)^n

Rearranging, we have:

(1.01075)^n = 1 ÷ 0.64

(1.01075)^n = 1.56

By converting the exponential function to a logarithm function, we have:

n = log_{1.01075}1.56

n = log_{1.01075}1.56

n = 41.59  approximately 42 months.

Therefore, it will take Calvin Johnson 42 months to pay off his credit card.

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Solution :

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The marginal product of the labor is the change in the quantity i.e pizza as Amy hires an additional worker.

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b).

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       0                            0              20                        0                          20

       1                            60             20                       30                         50

      2                            100             20                      60                       80

      3                            130             20                       90                       110

      4                            150            20                        120                      140

     5                             160            20                        150                      170

The fixed cost remains the same but the variable cost increases as one more worker is hired.

The law of the diminishing the marginal product of labor is determined by = total output increases at the decreasing rate as we increase the quantity of the labor.      

   

   

   

         

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