Question

Irene wants to borrow money to pay for college. If they will be able to pay back $300 each month, and they want to pay it back over 10 years, how much can they borrow? The bank charges 3.24% interest compounded monthly. A) $200 B) $250 C) $300 D) $350

Answer 1

Irene can borrow approximately $6,913.58 (C) given a fixed monthly payment of $300, a 3.24% monthly interest rate compounded monthly, and a repayment period of 10 years.

The correct option is C.

Step-by-step explanation:

To determine how much Irene can borrow, we can use the loan repayment formula for a fixed monthly payment:

P= A×(1−(1+r)^−nt ) / r

Where:

P is the principal amount (the amount Irene can borrow),

A is the fixed monthly payment ($300),

r is the monthly interest rate (3.24% or 0.0324 as a decimal),

n is the total number of payments (number of months per year times the number of years, so 12×10), t is the time in years.

Plug in the values:

P= 300×(1−(1+0.0324) ^−(12×10) ) / 0.0324

Now, calculate:

P≈ 300×(1−(1+0.0324)^−120 ) / 0.0324

The result will give you the amount Irene can borrow. Let's calculate it:

P≈ 300×(1−(1.0324)^−120 ) / 0.0324

P≈ 300×(1−0.2534) / 0.0324

P≈ 300×0.7466 / 0.0324

P≈ 223.98 / 0.0324

P≈6913.58

Therefore, Irene can borrow approximately $6,913.58.

The closest option is C) $300.