Madison has a mortgage of 300,000 through the Tangerine Bank...

Madison has a mortgage of $300,000 through the Tangerine Bank for a vacation property. The mortgage is repaid by end of month payments with an interest rate of 4.5% compounded monthly for a term of 5 years, amortized over 15 years. At the end of the 5-year term, she will renew the mortgage for another 5-year term at a new, lower interest rate of 3.7% compounded monthly. Enter ONLY POSITIVE VALUES for ALL ANSWERS, rounded to two decimal places. 1) What are the end of month payments before the renewal of the mortgage? $ 2) What is the balance when the mortgage is renewed? $ 3) What will be the new end of month payments after the mortgage is renewed? $

Transcript

00:01 Hi, here for the question the formula which we are going to use to calculate end of month payment for the initial mortgage is p equals to r p0 upon 1 minus 1 plus r to the power minus nt.

00:15 Now here in our case we have p as our monthly payment p0 which is initial principal of 30 ,000 dollars and further rate of interest r is equal to 4 .5 percentage which is equal to 4 .5 percentage upon 12 as we are calculating annual rate of interest this is equal to 0 .0375 n is the number of period so n is equal to 12 as we are compounding monthly and the total time t is equal to 15 into 12 which is equal to 118.

00:48 Here 12 because we are calculating according to the monthly cycle.

00:53 So here in our case substituting the value in our above formula here we have p equals to 0 .0375 into 300 ,000 divided by 1 minus 1 plus 0 .0375 to the power minus 180.

01:11 So by calculating this value we can say that we got our monthly principal amount p equals to 1620 .18 dollars.

01:21 So here this is the solution of the first part.

01:23 Now we need to find the remaining balance the formula to calculate balance b equals to p into 1 minus 1 plus r to the power minus nt upon calculating the balance we have p is equal to 1620 .18 dollars further the rate of interest r is equal to 3 .7 percentage which can be further written as 3 .7 upon 12 which is equal to 0 .3083 and here in the next step we have number of years is equal to 5.

01:54 So time period t is equal to 5 into 12 which is equal to 60.

01:58 So here substituting the value in our above formula we have balance b is equal to 1620 .18 into 1 minus 1 plus 0...

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