Nyasha used the Quantitative Reasoning Process to create a plan to pay off his student loans of $8,125. The interest rate on his loan is 13.5% annually and he plans to make monthly payments of $138.84 for 8 years. Complete months 1 and 2 of the amortization table below. Month Beginning Balance Payment: To Interest Payment: To Principal Ending Balance1 2 ?? 3 How much of Nyasha's payment goes to Interest in Month 2?(Round your FINAL answer to the nearest cent. Do not include the dollar sign.)
Question
Nyasha used the Quantitative Reasoning Process to create a plan to pay off his student loans of 138.84 for 8 years. Complete months 1 and 2 of the amortization table below. Month Beginning Balance Payment: To Interest Payment: To Principal Ending Balance1 2 ?? 3 How much of Nyasha's payment goes to Interest in Month 2?(Round your FINAL answer to the nearest cent. Do not include the dollar sign.)
Solution
To calculate the interest for the first month, we use the formula:
Interest = Principal x Rate x Time
Where:
- Principal is the initial loan amount ($8,125)
- Rate is the annual interest rate (13.5% or 0.135 as a decimal)
- Time is the length of time the money is borrowed (1 month or 1/12 of a year)
So, for the first month:
Interest = 91.40
The rest of the payment goes to the principal. So, the payment to the principal in the first month is:
Payment to Principal = Total Payment - Interest Payment to Principal = 91.40 = $47.44
The ending balance after the first month is then:
Ending Balance = Beginning Balance - Payment to Principal Ending Balance = 47.44 = $8077.56
For the second month, we repeat the process using the ending balance from the first month as the new principal:
Interest = 90.73
So, $90.73 of Nyasha's payment goes to interest in Month 2.
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