Question

britta has been accepted into a 2-year medical assistant program at a career school. she has been awarded a $6,000 unsubsidized 10-year federal loan at 4.29%. she knows she has the option of beginning repayment of the loan in 2.5 years. she also knows that during this non-payment time, interest will accrue at 4.29%. suppose that britta decided to take out a private loan for $12,000 for which loan payments start as soon as the loan amount is deposited in her account and continue for 10 years. the interest rate is 6.1%. a. determine her monthly payment. b. what is the total amount she will pay back? c. what is the total interest amount?

Answer 1

Britta's monthly private loan payment can be calculated using an amortization formula taking into account the principal amount, monthly interest rate, and total number of payments. The total amount paid and total interest over the 10-year period can then be derived from this monthly payment.

Step-by-step explanation:

To calculate Britta's monthly payment on her private loan of $12,000 with an interest rate of 6.1%, we need to use the formula for an amortizing loan which includes both principal and interest. This requires converting the annual interest rate to a monthly rate by dividing it by 12, and then utilizing the number of payments (10 years of monthly payments equals 120 payments).

The formula for the monthly payment (M) is derived from the amortization formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where P is the principal amount ($12,000), i is the monthly interest rate (6.1%/12), and n is the total number of payments (120).

Once the monthly payment is calculated, multiply it by 120 to find the total amount repaid over 10 years. To find the total interest paid, subtract the original loan amount ($12,000) from the total repaid.