Question

Magnus wants to borrow $26,000 to remodel his kitchen. He is hoping that his monthly payment will be no more than $372. The bank is offering a 4.3% loan. What will the length of his loan be if he is able to secure a $372 monthly payment?

Answer 1

About 81 months

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