Question

69. Suppose that you currently have one credit card with a balance of $10,000 at an annual rate of 24.00% interest. You have stopped adding any additional charges to this card and are determined to pay off the balance. You have worked out the formula bbn = b0r n − R(1 + r+r2 +....+ r n−1), where b0 is the initial balance, bn is the balance after you have maden payments, r= 1 + i, wherei is the monthly interest rate, and R is the amount you are planning to pay each month.

a. What is the monthly interest rate i ? What is the growth rate, r ?

Answer 1

`i = 1,8087 %`

`r = 1.018`

Explanation:

For an effective annual rate j you have that the monthly interest rate can be related to it as:

`(1+i)^(12)  = 1+j`

Solving for i:

`i=\sqrt[12]{1+j}  -1`

replacing j = 24% => i = 1,8087 %

So growth rate r would be:

`r = 1 + i = 1.018`