What's More: Quarter 2 - Module 7: Deferred Annuity

Quarter 2 - Module 7: Deferred Annuity
*The text color of your answers should be in “BLUE”
What’s More
Activity 1.1
1. Payment of ₱ 3,000.00 every 3 months for 8 years that will start 6 years.
Time Diagram Answer
23 periods or 23 months
interval
3. Payment of ₱ 700.00 every month for one (1) year that will start at the end of the
third month
Time Diagram Answer
2 periods or 2 months
interval
Activity 1.2
1. A group of college students decided to invest the money they earned from the
fund-raising project. After 6 months from today, they want to withdraw from this
fund ₱ 10,000.00 quarterly for 1 year to fund for community service. How much is
the present total deposit if the interest rate is 4% converted quarterly?
Given:
R = ₱ 10,000.00
r = 0.04
t=1
m=4
Number of artificial payments: k = mt = 1
Number of actual payments: n = mt = (4)(1) = 4
𝑖4 0.04
Interest rate per period:𝑗 = 𝑚 = = 0.01
4
−(𝑘+𝑛)
1 − (1 + 𝑗) 1 − (1 + 𝑗)−𝑘
𝑃=𝑅 −𝑅
𝑗 𝑗
1−(1+0.01)−(1+4) 1−(1+0.01)−1
= 10,000( 0.01
− 0.01
)
= ₱ 38,633.32
What I Have Learned
A. Fill in the blanks to make each statement true.
1. A deferred annuity is an annuity whose payments starts in more than
period from the present.
2. Each payment in an annuity is called the periodic payment.
3. A deferred annuity is an annuity whose first payment takes place at some
predetermined time k + 1.
4. In retirement planning, payments on income taxes are deferred until you withdraw
the money.
B. Answer the following questions.

1. What are the benefits of a deferred annuity?
Tax-deferred growth. You will pay no income taxes on the earnings from your
annuity investments until you begin making withdrawals or receiving periodic
payments. Unlimited contributions, choice of investment options, no mandatory
withdrawals, death benefits and lifetime income benefits are some as well.
2. Is a deferred annuity a good investment?

Annuities are insurance contracts designed to supplement retirement
income. Tax-deferral, death benefits and lifetime income are among the key
benefits of annuities. But they might not hold much value for you if you have a
pension and no heirs. Like any financial instrument, annuities play a specific role
in an investment portfolio, and deciding whether an annuity is a good investment
for you requires sound financial planning and clear goals. If you end up living a
very long life, a deferred annuity can keep you from running out of money too soon.
It can also be a good thing to buy while you're still middle-aged and working,
setting it up to pay you throughout your retirement.
3. What is the difference of grace period and deferment?

Both grace periods and deferments are periods of time during which a
borrower does not have to pay a lender money toward a loan. Grace periods tend
to be built into loan terms, whereas most deferments require application and
documentation. Deferring loan payments does not generally stop interest from
accumulating, so it can be quite impactful on the loan interest owed, depending on
the loan's terms.
C. Explain the basic types of deferred annuities: fixed, indexed, variable, and
longevity.
A fixed annuity is an insurance contract that guarantees the insurer will pay the
purchaser a guaranteed, fixed interest rate on their contributions to the annuity for
a specific period of time. Fixed annuities are lower risk than variable annuities and
can provide a steady stream of income in retirement.
An indexed annuity, also known as a fixed-index annuity, is a type of annuity whose

income payments are tied to a stock index, such as the S&P 500. Indexed annuities
perform well when the financial markets perform well. People often refer to indexed
annuities as hybrids of fixed and variable annuities.
A variable annuity is a tax-deferred retirement vehicle that allows you to choose

from a selection of investments, and then pays you a level of income in retirement
that is determined by the performance of the investments you choose.
Longevity annuities (aka. Deferred Income Annuities) are contracts between an

individual and an insurance company. The insured party deposits a premium
payment into the contract today and in exchange, receives a guaranteed income
stream for life beginning at a pre-determined future date.
The income stream will be based upon the premium deposited, the age of the
contract owner, their life expectancy, and the date/time frame in which the income
will be paid. Market fluctuations will not impact the income payments received. In
some cases, contract owners will be permitted to make additional contributions to
their annuities. These additional payments will impact the income received.
What I Can Do
1. Planning to give his son a car as a gift when he graduates from college 2 years
from now, Adam decides to set aside a fund to enable him to pay the expected
monthly amortization of ₱ 21,500.00 every month for 3 years. If a bank offers to
pay an interest of 7.5% compounding monthly, how much should be set aside in
order to achieve his plan?
Given:
R = ₱ 21,500.00
r = 0.075
t=3
m = 12
Number of artificial payments: k = 23

𝑖4 0.075
Interest rate per period:𝑗 = 𝑚 = = 0.00625
12
1 − (1 + 𝑗)−(𝑘+𝑛) 1 − (1 + 𝑗)−𝑘
𝑃=𝑅 −𝑅
𝑗 𝑗
1−(1+0.00625)−(23+36) 1−(1+0.00625)−23
= 21,500( − )
0.00625 0.00625
= ₱ 598,901.91 should be set aside in order to achieve his plan.
Additional Activities
3. Kim’s savings may allow her to withdraw ₱ 50,000.00 semi-annually for 5 years
starting at the end of 5 years. How much her savings, if the interest rate is 8%,
converted semi-annually?
Given:
R = ₱ 50,000
r = 0.08
t=5
m=2
Number of artificial payments: k = 9
𝑖4 0.08
Interest rate per period:𝑗 = = = 0.04
𝑚 2
−(𝑘+𝑛)
1 − (1 + 𝑗) 1 − (1 + 𝑗)−𝑘
𝑃=𝑅 −𝑅
𝑗 𝑗
1−(1+0.04)−(9+10) 1−(1+0.04)−9
= 50,000( − )
0.04 0.04
= ₱ 284,930.39

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Quarter 2 - Module 7: Deferred Annuity

*The text color of your answers should be in “BLUE”

B. Answer the following questions.

2. Is a deferred annuity a good investment?

3. What is the difference of grace period and deferment?

An indexed annuity, also known as a fixed-index annuity, is a type of annuity whose

A variable annuity is a tax-deferred retirement vehicle that allows you to choose

Longevity annuities (aka. Deferred Income Annuities) are contracts between an

Number of artificial payments: k = 23

= ₱ 598,901.91 should be set aside in order to achieve his plan.

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