Annuity Immediate vs Annuity Due | Exam FM | Financial Mathematics Lesson 14 - JK Math

Summary

This educational video script explores the concepts of annuity immediate and annuity due, explaining the difference in payment timing and valuation points. It delves into the formulas for calculating the future and present values of both types, simplifying them for easier application. The script also introduces the concept of a perpetuity due and provides an example problem to illustrate the calculations for an annuity due with payments made at the beginning of each period.

Takeaways

• 📚 The script discusses the difference between annuity immediate and annuity due, two types of annuities based on when payments are made.
• 🔢 Annuity immediate formulas are for payments made at the end of each period, while annuity due formulas account for payments made at the beginning of each period.
• 📈 The future value of an annuity immediate is calculated immediately after the last payment, whereas for an annuity due, it's one period after the last payment.
• 🕒 The present value of an annuity immediate is found at the beginning of the first period, before the first payment, while for an annuity due, it includes the first payment.
• 📉 The valuation point for both present and future values of an annuity due is one period later than for an annuity immediate.
• 💡 The script introduces formulas for calculating the present and future values of both annuity immediate and annuity due, highlighting the slight adjustments needed for due payments.
• ✍️ The formulas for annuity due are simplified to avoid confusion with annuity immediate notations, making them more user-friendly.
• 🔑 A key formula derived is the present value of a perpetuity due, which is calculated as 1 divided by (1 minus the present value factor).
• 🧮 An example problem is provided to illustrate the calculation of both the present and future values of an annuity due with a series of payments.
• 📝 The importance of matching the frequency of payments with the compounding frequency of the interest rate is emphasized for accurate annuity calculations.
• 🔗 Additional resources such as example problems and further explanations are available through links provided in the video description.

Q & A

What is an annuity immediate?

An annuity immediate is a type of annuity where payments are made at the end of each payment period. The future value of an annuity immediate is calculated immediately after the last payment is made.

What is the formula for the future value of an annuity immediate?

The formula for the future value of an annuity immediate is the series of payments multiplied by the future value interest factor, which is (1 + i)^n - 1 divided by i, where i is the interest rate and n is the number of periods.

How is the present value of an annuity immediate calculated?

The present value of an annuity immediate is calculated at the beginning of the first period, using the formula which involves the present value interest factor for an annuity, which is 1 - (1 + i)^-n divided by i.

What is the difference between an annuity immediate and an annuity due?

The main difference between an annuity immediate and an annuity due is the timing of the payments. For an annuity immediate, payments are made at the end of each period, while for an annuity due, payments are made at the beginning of each period.

What is the formula for the present value of an annuity due?

The present value of an annuity due is calculated using a formula that adjusts the present value of an annuity immediate by compounding it forward by one period using the interest rate.

How do you calculate the future value of an annuity due?

The future value of an annuity due is calculated by taking the future value of an annuity immediate and then compounding it forward by one period using the interest rate.

What is a perpetuity due?

A perpetuity due is a type of annuity where payments never end and are made at the beginning of each period. The present value of a perpetuity due is calculated by taking the present value of a perpetuity immediate and adjusting it for the timing of payments.

What is the present value factor and how is it used in annuity calculations?

The present value factor is used to discount future cash flows to their present value. It is equal to 1 divided by (1 + i)^n, where i is the interest rate and n is the number of periods. It is used in both annuity immediate and annuity due calculations.

How do you simplify the formulas for the future value and present value of an annuity due?

The formulas for the future value and present value of an annuity due can be simplified by using the relationship between the interest rate and the discount rate, which allows you to express the formulas in terms of the present value factor (1 - v) instead of the interest rate (i).

Can you provide an example of calculating the present and future values for an annuity due with a given set of payments and interest rate?

Sure, if you have payments of $60 invested each year for 10 years with an effective annual interest rate of 5%, you would use the annuity due formulas with these values to find the present value and future value after 10 years.

Why is it important to match the frequency of the interest rate with the payment frequency in annuity calculations?

It's important to match the frequency of the interest rate with the payment frequency to ensure that the calculations accurately reflect the time value of money. This consistency avoids discrepancies in the valuation of the annuity.