Question

In: Finance

You are planning on taking a loan for $ 49 ,000. You will repay the loan...

You are planning on taking a loan for $ 49 ,000. You will repay the loan in annual payments over the next 7 years and the loan has a stated interest rate of 6 %. For the very last payment on your loan, how much of this is repayment of principal? For example, if the loan payment is $400 of which $30 is interest and $370 is principal, your answer is $370. Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

Solutions

Expert Solution

Step-1:Calculation of Annual Payment
Annual Payment = Loan Amount/ Present Value of annuity of 1
= $       49,000 / 5.5823814
= $   8,777.62
Working:
Present Value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.06)^-7)/0.06 i 6%
= 5.5823814 n 7
Step-2:Preparation of Loan Amortization Schedule
Year Beginning Loan amount Interest Expense Annual Payment Reduction in Principal Ending Loan Balance
1 $ 49,000.00 $ 2,940.00 $ 8,777.62 $ 5,837.62 $ 43,162.38
2 $ 43,162.38 $ 2,589.74 $ 8,777.62 $ 6,187.87 $ 36,974.51
3 $ 36,974.51 $ 2,218.47 $ 8,777.62 $ 6,559.15 $ 30,415.37
4 $ 30,415.37 $ 1,824.92 $ 8,777.62 $ 6,952.69 $ 23,462.67
5 $ 23,462.67 $ 1,407.76 $ 8,777.62 $ 7,369.86 $ 16,092.82
6 $ 16,092.82 $     965.57 $ 8,777.62 $ 7,812.05 $   8,280.77
7 $   8,280.77 $     496.85 $ 8,777.62 $ 8,280.77 $            0.00
Thus,
Repayment of Last payment in the form of Principal $ 8,280.77

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