PLEASE SHOW WORK A fully amortizing loan has the following terms and conditions:

Question

PLEASE SHOW WORK

A fully amortizing loan has the following terms and conditions:

Interest Rate:                      6% per annum

Term:                                   20 years

Original Loan Amount:    $250,000

What would be the monthly payment?

What would be the total amount of payments made over the 20 years? The total interest paid over 20 years? The total principal paid over 20 years?

What would be the outstanding loan balance after eight years? How much interest and principal have been paid over the first eight years?

If at the end of eight years you pay an extra principal payment of $15,000, what is the remaining term of this loan assuming your payments found in part a continue?

If at the end of eight years you pay an extra principal payment of $15,000, what is the new monthly payment if the remaining loan is not shortened (total term of 20 years is maintained)?

Explanation / Answer

Ans. Monthly payment = Principal X r(1+r)n

                                                                            (1+r)n -1

                                    = $250000 X 6%/12 (1+.06/12)240

                                                                    (1+.06/12)240-1

                                    = $1791.08

Total amt of payment made over the 20years = (1791.08X240) =$429859.20

Total Principal payment over the 20years = $250000

Total interest payment over the 20years = (429859.20-250000) =$179859.20

-Total amt paid over the eight years (1791.08X8X12)=$171943.68

-Interest payment over the eight year =$105483.68

-Principal payment over the eight year ($171943.68-105483.68) = $66460

-Principal outstanding end of eight year ($250000-66460)=$183540

If end of eight year extra payment is made of $15000, and monthly payment is same $1791.08

Calculation of Remaining tenure of loan

Outstanding principal after extra payment end of eight year (183540-15000)=$168540

          $1791.08                  =$168540 X .06/12(1+.06/12)n

                                                            (1+.06/12)-n

                                          = 127 month or 10 years 7 month (Approx.

Calculation of monthly payment if end of eight pay extra $15000

outstanding principal =$168540

Remaining tenure is (20-8) =12 years

EMI                = $168540X .06/12(1+.06/12)144

                                            (1+.06/12)144-1

                     = $1644.70

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