Question

A loan is repaid with monthly payments that start at $320 at the end of the first month and increase by $5 each month until a payment of $950 is made, after which they cease. If the annual effective interest rate is 4%, find the amount of principal in the sixtieth payment.

Answer 1

The amount of principal in the sixtieth payment is $670.

Step-by-step explanation:

To find the amount of principal in the sixtieth payment, we need to first calculate the monthly payments using the given information. We know that the monthly payments start at $320 and increase by $5 each month until a payment of $950 is made. Let's calculate the total number of payments and the common difference:

Total number of payments = (950 - 320) / 5 + 1 = 126

Common difference = 320 + (125 * 5) = 895

Now, we can use the formula for the sum of an arithmetic series to find the amount of principal in the sixtieth payment:

Amount of principal in the sixtieth payment = First term + (nth term - first term) / 2 = 320 + (60 * 5) / 2 = $670