SOLVING PROBLEMS ON BUSINESS AND CONSUMER LOANS (AMORTIZATION AND MORTGAGE) || GENERAL MATHEMATICS

The video defines outstanding balance as the present value of all remaining payments, referred to as the prospective method. An example involves Mrs. C, who has a loan with a 12% interest rate compounded monthly and a monthly amortization of 11,122.22 pesos for 5 years (60 payments). To find the outstanding balance after the 12th payment, we calculate the remaining payments (60 - 12 = 48). Using the outstanding balance formula, the amount after the 12th payment is found to be 422,354.73 pesos.

This section introduces the concepts of amortization and mortgage. Amortization is defined as a method of repaying a loan, including principal and interest, in equal installments over regular intervals. Mortgage is explained as a loan secured by collateral, where the borrower agrees to specific payment terms. The 'outstanding balance' refers to the remaining debt at a particular time.

An example demonstrates how to calculate the future value of a business loan. Mr. Garcia borrowed 1 million pesos at a 7% interest rate, to be repaid after one year. The principal amount is 1,000,000, the interest rate (j) is 0.07, and the term (n) is 1 year. Using the formula (Principal Amount) * (1 + j)^n, the future value to be paid is 1,070,000 pesos.

This part illustrates how to calculate the total interest paid on a car mortgage. A person borrowed 1,200,000 pesos for a car with a five-year mortgage and a monthly payment of 31,000 pesos. The total amount paid is calculated by multiplying the monthly payment by 12 months and then by 5 years (31,000 * 12 * 5 = 1,860,000). The total interest is the total amount paid minus the principal amount (1,860,000 - 1,200,000 = 660,000).

Here, the video explains how to find the amount of a mortgage after a down payment. If a house is sold for 3,000,000 pesos and requires a 20% down payment, the down payment is calculated as 20% of 3,000,000, which is 600,000 pesos. The mortgage amount is the cost price minus the down payment (3,000,000 - 600,000 = 2,400,000 pesos).

This section covers how to determine the monthly payment for a loan. Miss Result bought a car with a loan amount of 400,000 pesos, an interest rate of 9% compounded monthly, over a term of 3 years. The nominal rate is 0.09, and monthly compounding means n = 36 (3 years * 12 months). The rate of interest per conversion period (j) is 0.09/12 = 0.0075. Using the formula for regular payments, R = P / [ (1 - (1 + j)^-n) / j ], the monthly payment is calculated to be 12,719.89 pesos.