FINDING THE PRESENT VALUE OF GENERAL ANNUITY || GRADE 11 GENERAL MATHEMATICS Q2

Summary

In this video lesson, the instructor explains how to calculate the present value of a general annuity. Using clear examples, the lesson covers key formulas, including the present value formula and how to convert nominal interest rates to equivalent rates per payment interval. Three detailed examples are provided: calculating a loan's present value with quarterly compounding, determining the cost of a TV set with semi-annual compounding, and comparing the cash price to installment payments for a product. Viewers are guided through each step to better understand annuities and how interest impacts financial decisions.

Takeaways

• 😀 The video focuses on how to calculate the present value of a general annuity.
• 😀 A general annuity is a series of regular payments made over a fixed period, and the present value represents the total value of those payments at the current time.
• 😀 The formula for present value of a general annuity is: PV = R × (1 - (1 + i)^(-n)) / i, where R is the regular payment, i is the interest rate per period, and n is the number of periods.
• 😀 The nominal interest rate may need to be converted to an equivalent interest rate for the payment interval, depending on the compounding period.
• 😀 To convert the nominal interest rate to the equivalent interest rate per period, use: i = (r / m), where r is the nominal rate and m is the number of compounding periods per year.
• 😀 The video provides an example of borrowing money with annual payments and compounded quarterly interest, demonstrating how to find the present value using the formula.
• 😀 In the first example, a person borrows 100,000 pesos, with annual payments of 3,873.76 pesos for 3 years at an 8% nominal interest rate compounded quarterly.
• 😀 Another example calculates the present value of a TV set, where Mrs. Remoto pays 3,000 pesos monthly for six months with 9% interest compounded semi-annually, resulting in a present value of 17,545.08 pesos.
• 😀 The third example compares the total cost of a TV set bought through installments versus the cash price, showing that the installment plan costs more due to the added interest.
• 😀 Key concepts include the importance of understanding how to adjust for the payment frequency and compounding periods when applying the annuity formula to real-life financial scenarios.
• 😀 The video teaches viewers how to use a scientific calculator to perform the necessary calculations and find the present value of annuities in different payment scenarios.

Q & A

What is the primary topic discussed in the video?

The video focuses on calculating the present value of a general annuity, including the use of formulas and practical examples to illustrate the process.

What is the formula for calculating the present value of a general annuity?

The formula for calculating the present value (PV) of a general annuity is: PV = R × (1 - (1 + i)^-n) / i, where R is the regular payment, i is the equivalent interest rate per payment interval, and n is the number of payment periods.

How do you convert a nominal interest rate to an equivalent interest rate for a specific payment interval?

To convert the nominal interest rate to an equivalent interest rate for a specific payment interval, use the formula: i = (r / m2) × (1 + r / m1)^(m2 / m1) - 1, where r is the nominal rate, m1 is the payment interval, and m2 is the compounding period.

In Example 1, how much money did the borrower borrow, given that they agreed to pay 38,373.76 pesos annually for 3 years at 8% interest compounded quarterly?

The borrower borrowed 100,000 pesos. This was calculated using the present value formula with the provided interest rate and payment details.

What is the equivalent interest rate for the monthly payment interval in Example 2, where the nominal rate is 9% compounded semi-annually?

The equivalent interest rate for the monthly payment interval in Example 2 is 0.00975879. This was derived using the formula to convert the nominal interest rate compounded semi-annually to a monthly interval.

How much is the cost of the TV in Example 2 if the present value is 17,545.08 pesos?

The cost of the TV is 17,545.08 pesos, which was calculated using the present value formula, taking into account the regular monthly payments of 3,000 pesos over 6 months with a 9% nominal interest rate compounded semi-annually.

In Example 3, how do you compare the cost of the TV set when bought in cash versus monthly installments?

In Example 3, the TV set is priced at 16,000 pesos for cash. When purchased with monthly installments of 2,950 pesos for 6 months, with 12% interest compounded semi-annually, the present value (total cost) of the installment plan is 17,110.84 pesos, which is higher than the cash price.

What is the importance of converting the nominal interest rate when calculating present value for different payment intervals?

Converting the nominal interest rate is important to accurately reflect the interest rate for the specific payment interval. This ensures that the present value calculation is correct when the payment and compounding periods differ.

In the formula for calculating the present value of a general annuity, what do each of the variables represent?

In the present value formula, R represents the regular payment amount, i is the equivalent interest rate per payment interval, and n is the number of payment periods. These values are used to determine the current worth of future payments.

Why is it necessary to use a scientific calculator for some of the examples in the video?

A scientific calculator is necessary for accurately performing complex calculations such as exponentiation and logarithms, which are involved in converting interest rates and calculating the present value of annuities.