Present Value of Deferred Annuity

Bringing it Back to the Present: Calculating the Present Value of a Deferred Annuity

We've explored deferred annuities and the period of deferral, understanding how to pinpoint when those future payments kick in. Now, let's bring those future payments back to the present! Lesson 7 dives into calculating the present value of a deferred annuity, figuring out how much those future payments are worth in today's money.

Get ready to:

• Apply the concept of discounting to deferred annuities, understanding how time impacts their present value.

• Master the formula for calculating the present value of a deferred annuity.

• Solve real-world problems involving deferred annuities, such as determining how much you need to invest today to fund a future stream of income.

• Visualize deferred annuities using timelines, making it easier to grasp the timing of payments and the discounting process.

By the end of this lesson, you'll be a pro at evaluating deferred annuities, understanding their value in today's terms and making informed financial decisions for a secure future. Let's unlock the present value of those future promises!

Activity: The Time Traveler's Dilemma

Scenario: Imagine you've stumbled upon a time machine and have two options:

Option A: Receive ₱100,000 today.

Option B: Receive ₱15,000 per year for 10 years, starting 5 years from now.

Which option seems more valuable? Explain your reasoning. Consider the time value of money and the delayed gratification aspect of Option B.

This lesson equips you with the knowledge to calculate the present value of deferred annuities and visualize their payment timelines.

Example 1

Problem: On his 40th birthday, Mr. Ramos decided to buy a pension plan for himself. This plan will allow him to claim P10,000 quarterly for 5 years starting 3 months after his 60th birthday. What one-time payment should he make on his 40th birthday to pay off this pension plan, if the interest rate is 8% compounded quarterly. 

Solution:

R = P10,000

r = 8% = 0.08

i = r/m = 0.08/4 = 0.02

m = 4 (compounded quarterly)

t = 5 years

n = mt = 5 years * 4 payments/year = 20 payments

period of deferral = k = 80

Using the formula given above, substitute all the values and calculate for the present value of Mr. Ramos monthly pension.

Therefore, P = P33,538.38

Example 2

Problem: A credit card company offers deferred payment options for the purchase of any appliance. Rose plans to buy a smart television set with monthly payments of P4,000 for 2 years. The payments will start at the end of 3 months. How much is the cash price of the TV set if the interest rate is 10% compounded monthly? 

Solution:

R = P4,000

r = 10% = 0.10

m = 12 (compounded monthly)

t = 2 years

i = r/m = 0.10/12

n = 2 years * 12 payments/year = 24 payments

period of deferral = k = 2

*Substitute all values at the formula above.

Therefore, the cash price of the TV is approximately P85,256.56

Example 3

Problem: Mr. Quijano decided to sell their farm and to deposit the fund in a bank. After computing the interest, they learned that they may withdraw P480,000 yearly for 8 years starting at the end of 6 years when it is time for him to retire.How much is the fund deposited if the interest rate is 5% converted annually? 

Solution:

R = P4,000

m = 1

r = 5% or 0.05

t = 8 years

i = r/m = 0.05/1 = 0.05

n = mt = (1)(8) = 8

k = 5

Using the formula and calculator, the P = P2,430,766.23

Ready to master the present value of deferred annuities? This assessment tests your ability to calculate the present value of deferred annuities using the appropriate formula and to construct time diagrams to visualize these concepts.

Lesson 7 Complete! Ready to put your annuity knowledge to the test? Head to the Module 2 Assessment!