PROBLEMS IN BUSINESS AND CONSUMER LOANS

Good afternoon, this is Sir Glenn. For our example number 1, Mr. Garcia borrowed 1 million pesos for the expansion of his business. The effective interest rate is 7%, and the loan is to be repaid in full after one year. How much is to be paid after 1 year? So you must, must not reach the given. So Mr. Garcia borrowed 1 million pesos, so this is the present value of money at 1 million pesos. And then 7%, this is the interest rate, so let this be J. It's 0.07% in decimal or 7%. We're going to find out how much is to be paid after 1 year. So this is the future value of money. The future value of money formula using the compound interest. The formula is F is equal to C times 1 plus I to N where N is equal to M times C and I is equal to J over M. So what's the story here? At M is, remember that this is the number of conversion period. So this is 1 year, that's M is equal to 1. So first we compute the N, N is 1, M is 1. And then C, it's pala, reaching C is also 1 year. The loan is to be repaid in full after 1 year. C is 1, so N is therefore equal to 1. Now for our I, I is equal to J over M. So J is 0.07 divided by M is equal to 1. So also I is equal to 0.07. Calculating for F, F is equal to C, 1 million pesos, times 1 plus I is 0.07 raised to N which is 1. So using our calculator, we do this by taking 1. So 1 plus 0.07 is 1.07 and then raised to 1 nat. We have 1,070,000 pesos. So this means that an amount of 1,070,000 pesos must be paid after 1 year. Example number 2, a person borrowed 1,200,000 pesos to buy a car. If his monthly payment is 31,000 pesos in a 5-year mortgage, find the total amount of money. So list more than you can give. So we have person borrowed 1,200,000 pesos. So this is the present value of money, so C. And then we have the monthly payment. So we have a monthly payment of 31,000 pesos. So empty na lang. But what are we going to find? We're going to find the total amount of interest. So first we calculate for the total amount paid in a 5-year period. So the formula here will be the monthly payment times we have 5 years. So we have a 5-year mortgage, five years. And then times since monthly payment, we convert yung 5 years, we multiply that to 12 pa. Okay, so empty times 5 times 12. So we have the total amount paid is 31,000 times 5 times 12. So using our calculator, this will give us 1,860,000. But we're going to find the total amount of interest. So the total amount of interest is the total amount paid minus the present value of money. So this one, 1,860,000 minus yung hiram nya, the borrowed money is 1,200 pesos. So using our calculator, this will give us 650,000 pesos. Example number 3. If a house is sold for 3,000,000 pesos and the bank requires a 20% down payment, find the amount of the mortgage. We find the given. The given are, we have the down payment rate. The down payment rate is 20% or 0.20. And then we have the cash price. That's the CP. The cash price is 3,000,000 pesos. Now, what are we gonna find? We're going to find the down payment first. The down payment is equal to the down payment rate times the cash price. Okay, so we have down payment rate at 0.2 times we have the 3,000,000. So this will give us the 600,000. Okay, now we find the amount of the loan or the amount of the mortgage. So the amount of the loan, let this be AL is equal to the cash price minus the down payment. So the cash price is 3,000,000 pesos. The amount of the house is 3,000,000 pesos minus the down payment. This is 600,000 pesos. Will give us 2,400,000 pesos. For our last example, Miss Casey bought a car. After paying the down payment, the loan amount is 400,000 pesos. It's a 9% compounded monthly interest rate. The loan term is 3 years. How much is the monthly payment? Let's write the given. The loan amount is 400,000 pesos. It's the present value of money. And then we have the 9% which is the day of 0.09 or 9%. And then our M. Our M is monthly. We have 12. So our N and M times T. So our M is 12. By the way, our T. T here is 3 years. T is equal to 3. 12 times 3. N is equal to 36. What are we gonna find? So how much is the monthly payment? This means that we are going to find the regular payment or the periodic payment. R. I'm not sure. The formula to be used here is simple and easy. So the regular payment or R is equal to T over 1 plus I raised to negative N All over the place. So we still have I here. I here is J over M. J is 0.09 in decimals divided by 12. I am, using our calculator, I'm not going to. Okay, so we're ready to solve for R. T is 400,000 pesos divided by 1 minus 1 plus 0.0075. Raised to negative N is 36. All over 0.0075. What's our R? Let's add 1 plus 0.0075 to 1 plus 0.0075. Raised to negative. This is the negative sign. - I got 36. Okay, that's equal. So the regular payment is 12,719.89 pesos. Thank you very much, sir. I hope you've learned from this lesson. This is it again. Hope to see you on my next upload. Keep safe and God bless.