Questions: You decide to quit using your credit card and want to pay off the balance of 6,300 in 2 years. Your interest rate is 15.05% compounded monthly. What will your monthly payments be?

You decide to quit using your credit card and want to pay off the balance of 6,300 in 2 years. Your interest rate is 15.05% compounded monthly.

What will your monthly payments be?

Transcript text: You decide to quit using your credit card and want to pay off the balance of $\$ 6,300$ in 2 years. Your interest rate is $15.05 \%$ compounded monthly. What will your monthly payments be?

Solution

Solution Steps

To find the monthly payments needed to pay off a credit card balance with compound interest, we can use the formula for the monthly payment on an amortizing loan. This formula takes into account the principal amount, the interest rate, and the number of payments. The interest rate needs to be converted to a monthly rate, and the total number of payments is the number of months over which the balance will be paid off.

Step 1: Given Values

We are given the following values:

Principal amount ($ P $): $ 6300 $
Annual interest rate ($ r $): $ 15.05\% = 0.1505 $
Time period ($ t $): $ 2 $ years

Step 2: Convert Interest Rate and Calculate Number of Payments

The monthly interest rate ($ r_m $) is calculated as: \[ r_m = \frac{r}{12} = \frac{0.1505}{12} \approx 0.0125416667 \] The total number of monthly payments ($ n $) over $ 2 $ years is: \[ n = 2 \times 12 = 24 \]

Step 3: Calculate Monthly Payment

The monthly payment ($ M $) can be calculated using the formula for an amortizing loan: \[ M = \frac{P \cdot r_m}{1 - (1 + r_m)^{-n}} \] Substituting the values: \[ M = \frac{6300 \cdot 0.0125416667}{1 - (1 + 0.0125416667)^{-24}} \approx 305.6156 \]