Answer:
About 81 months
Step-by-step explanation:
We'll have to use this formula: A = P x i(1 + i)ˣ / (1 + i)ˣ - 1
A = Montly payment (372)
P = Loan amount (26,000)
i = interest rate/12 (0.043/12 = 0.035833)
x = months (?)
372 = 26,000 x 0.035833(1 + 0.035833)ˣ / (1 + 0.035833)ˣ - 1
First, substitute (1 + 0.035833)ˣ for y just to make things easier
372 = 26,000 x 0.035833y / y - 1
Multiply both sides by y - 1
(y-1)(372 = 26,000 x 0.035833y / y - 1)
372y - 372 = 26,000 x 0.035833y
Divide both sides by y
(372y - 372)/y = (26,000 x 0.035833y)/y
372 - 372/y = 26,000 x 0.035833
Add 372/y to both sides
372 - 372/y = 26,000 x 0.035833
- 372/y - 372/y
372 = 93.1667 + 372/y
Subtract 93.1667 from both sides
372 = 93.1667 + 372/y
- 93.1667 - 93.1667
372 - 93.1667 = 372/y
Cross multiply
y = 372/(372 - 93.1667)
y = 1.33413
(1 + 0.035833)ˣ = 1.33413
log₁₋₀₀₃₅₈₃₃(1.035833ˣ) = log₁₋₀₀₃₅₈₃₃(1.33413ˣ)
x = 80.59418
