Respuesta :
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
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
[tex]n = log_{1.01075}1.56[/tex]
n = 41.59 approximately 42 months.
Therefore, it will take Calvin Johnson 42 months to pay off his credit card.
