4) A family buys a new house using a $200,000 mortgage at i(12) = 5.4% . They pl

Question

4) A family buys a new house using a $200,000 mortgage at i(12) = 5.4% . They plan to repay the mortgage with payments made at the end of each month for 25 years. a) Find their monthly payment b) Assuming that they follow the amortization schedule, find the outstanding balance on the loan at the end of the 4th year (immediately after the 48th payment). c) Find the amounts of interest and principal paid in the 49th payment, based on the original payment schedule. d) If they made an additional payment of $30,000 at the end of the 4th year but kept their remaining payment amount at the level calculated in part a), when do they expect to pay the loan off?

Explanation / Answer

PV of loan amount is $200,000. Interest rate is 5.4% compounded monthly.

Input the following in the financial calculator to calculate the PMT (per month payment)

PV = 200,000; FV = 0; n=25*12; 1/y = 5.4%/12; Calculate PMT = $1,216.26

Monthly schedule for 6 yeras have been shown below. We have calculated that the per month payment is 1216.26. Now interst payment will be 5.4%/12*Beginning Principle and remaining will be principle repaid in that month.

Now outstanding principle at the end of 4th year i.e. after 48th payment is $141,620 as shown in the cash flow below

Amount of principle is $392 and Interest payment is $824 as shown in cash below

Now since they made an additional payment of $30,000, outstanding principle is $141,620 - $30,000 = $111,620

Now input the following in the financial calculator

PV = 111620; FV = 0; 1/y = 5.4%/12; PMT = 1216.26; calculate n = 118.6 months i.e. it will take ~10 more years to completely payoff the loan.

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