pang aral ng maaga

1. SIMPLE ANNUITY

2. ANNUITY – a sequence of
payments made at
equal (fixed)
intervals or periods
of time.

3. Ang pantay pantay na
bayad o kita na
ibinabayad o
tinatanggap sa pantay
na pagitan ng
panahon. (regular

4. Example:
• Buwan-buwang hulog sa
house loan o car loan.
• Taunang pension na
tinatanggap ng retirado.
• Regular na hulog sa isang
insurance o investment
plan.

5. According to payment interval and
interest period
Example:
Buwanang hulog kung ang
interest ay buwanan din.

6. According to payment interval and
interest period
Example:
Nagbabayad ka buwan-buwan
pero ang interest ay kinukwenta
kada taon.

7. According to time of payment
Example:
Pagbabayad ng utang sa
bangko kada buwan (ang
hulog ay katapusan ng buwan).

8. According to time of payment
Example:
Pagbabayad ng renta ng bahay
(karaniwang bayad muna bago
tumira)

9. According to duration
Example:
May simula at may
katapusan ang pagbabayad o
pagtanggap ng pera.

10. According to duration
Nakadepende sa pangyayari.
Example:
• Habang buhay pa ang isang tao, magpapatuloy ang
bayad.
• Kapag hindi na natupad ang kondisyon ( namatay ang
isang tao, hihinto na ang annuity.

11. TERM OF ANNUITY (t) – time
between the first payment
interval and last payment
interval.
AMOUNT ( FUTURE VALUE) OF
AN ANNUITY (F) – sum of future
values of all the payments to be
made during the entire term of
the annuity.
REGULAR OR PERIODIC

12. PRESENT VALUE OF
ANNUITY (P) – sum of
present values of all the
payments to be made during
the entire term of the
annuity.

13. Annuities may be illustrated using
a time diagram. The time diagram
for an ordinary annuity (i.e.,
payment are made at the end of
the year is given below.

14. Example 1:
Suppose Mrs. Remoto would like
to save Php 3,000.00 every
month in a fund that gives 9%
compounded monthly. How much
is the amount or future value of
her savings after 6 months?

15. Given:
Periodic payment, R = Php 3,000.00
Term, t = 6 months
Interest rate per annum = 0.09
Number of conversions per year, m = 12
Interest rate per period,
j = 0,09/12 = 0.0075
n = mt = (12)(0.5) = 6 periods
Find: amount (future value) at the end of
the term, F = ?

20. Example 2:
In order to save for her high
school graduation, Marie decided
to save Php 200.00 at the end of
each month. If the bank pays
0.25% compounded monthly, how
much will her money be at the
end of 6 years.

24. Example 3:
Mr. Ribaya paid Php 200,000.00
as down payment for a car. The
remaining amount is to be settled
by paying Php 16,200.00 at the
end of each month for 5 years. If
the interest is 10.5% compounded
monthly, what is the cash price of
his car?

27. The FUTURE VALUE of an
annuity is total accumulation of the
payments and interest earned.
The PRESENT VALUE of an
annuity is the principal that must be
invested today to provide the regular
payment of an annuity.

29. Example 4:
Paolo borrowed Php 100,000.00.
He agrees to pay the principal
plus interest by paying an equal
amount of money each year for 3
years. What should be his annual
payment if interest is 8%
compounded annually?