Respuesta :
Answer:
It will take Meryl 15.09 months to pay off the balance.
Step-by-step explanation:
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or the cost of the new baseball equipment = $2000
P = Monthly payment = $150
r = Monthly interest rate = annual percentage rate (APR) / 12 = 19% / 12 = 0.19 / 12 = 0.0158333333333333
n = number of months it will take Meryl to pay off the balance = ?
Substitute the values into equation (1) and solve for n, we have:
2000 = 150 * ((1 - (1 / (1 + 0.0158333333333333))^n) / 0.0158333333333333)
2000 / 150 = (1 - (1 / 1.0158333333333333)^n) / 0.0158333333333333
13.3333333333333 = (1 - 0.984413453650536^n) / 0.0158333333333333
13.3333333333333 * 0.0158333333333333 = 1 - 0.984413453650536^n
0.21111111111111 = 1 - 0.984413453650536^n
0.984413453650536^n = 1 - 0.21111111111111
0.984413453650536^n = 0.78888888888889
loglinearize both sides, we have:
nlog0.984413453650536 = log0.78888888888889
n = log0.78888888888889 / log0.984413453650536
n = -0.102984160720249 / -0.00682245957075587
n = 15.0948729929724
Rounding to 2 decimal places, we have:
n = 15.09
Therefore, it will take Meryl 15.09 months to pay off the balance.
