sample ppt

1. Future Value
of Simple
Annuity

2. OBJECTIVES:
Define annuity payment;
Differentiate simple annuity
from general annuity; and,
Solve problems involving future
value of simple annuity.

3. Examine the
term
1.Rental payment
2.Monthly pension
3.Monthly payment for car loan
4.Educational plan

4. Annuities may be classified in
different ways, as follows.
ACCORDING TO PAYMENT INTERVAL AND
INTEREST PERIOD
Simple annuity- an annuity where the payment
intervals is the same as the interest period.
General Annuity- an annuity where the payment
intervals is not the same as the interest period.

5. ACCORDING TO TIME OF PAYMENT
Ordinary annuity- an annuity which payment
are made at the end of each payment interval.
Contingent Annuity- an annuity which in the
payment extend over an indefinite or
indeterminate length of time.
ACCORDING TO DURATION
Annuity Certain- an annuity in which
payments begin and end at definite times,

6. 1.Example of a simple annuity –
installment payment for an appliances at
the end of each month with interest
compounded monthly.
2.Example of a general annuity –
installment payment for an appliances at
the end of each month with interest
compounded annually.

7. Future Value of Simple Ordinary Annuity
(F)
F = R ( 1 + j)n
– 1
J
Where:
R - is the regular payment
j - is the interest rate per period, and
n - is the number of payments

8. Example 1. Suppose Mrs. Remoto would like to save
₱3000 at the end of each month, for six months, in a
fund that gives 9% compounded monthly. How
much is the future value of her savings after 6
months?
Given: R = ₱3000
term t = 6 months
interest rate per annum i(12)
= 0.09
number of conversions per year m = 12
interest rate per period j = = 0.0075
n = mt = (12 * 6months ()) = 6

9. Find: future value at the end of the term, F
F = R ( 1 + j)n
– 1
j
= 3,000 ( 1 + 0.0075)6
– 1
0.0075
F = ₱18,340.89

10. Example 2. In order to save for her high school
graduation, Marie decided to save ₱200 at the end of
each month. If the bank pays 0.250% compounded
monthly, how much will her money be at the end of
6 years?
Given: R = 200
t = 6 years
i(12)
= 0.250% = 0.0025
m = 12
j = = 0.0002083
n = mt = (12)(6) = 72 periods

11. Practice:
1. Mr. Cruz saves ₱1,500 at the end of each month
in a savings account that earns 10% annual
interest compounded monthly.
How much will he have in the account after 3
years?
2. A company sets aside ₱10,000 every quarter to
replace its office equipment. If the fund earns
8% interest compounded quarterly, what will be
the value of the fund after 5 years?
62,634.64 or 62,635
242,973.70 or 242,974

12. ACTIVITY:7
Directions: Find the future value of the following. Write your answer on
a separate sheet of paper.
1. Quarterly payments of 2,000 for 5 years with interest rate of 8%
₱
compounded quarterly.
2. Semi-annual payments of 8,000 for
₱ 12 yearswith interest rate of
12% compounded semi-annually
3. Suppose Mrs. Remoto would like to save ₱3,000 every month in a
fund that gives 9% compounded monthly. How much is the amount
or the future value of her savings after 6 months.
4. Peter started to deposit 5,000 quarterly in a fund that pays 1%
₱
compounded quarterly. How much will be in the fund after 6 years?

13. Present
Value of
Simple
Ordinary
Annuity (P)

14. Present Value of Simple Ordinary
Annuity (P)
P= R [1-( 1 + j)-n
] Cash Value= DP+P
j
Where R is the regular payment
j is the interest rate per period,
and
n is the number of payments

15. Example 1: Mr. Dela Cruz paid ₱200,000 as a down
payment for a car. The remaining amount is to be
settled by paying ₱16,200 at the end of each month
for 5 years. If interest is 10.5 % compounded
monthly, what is the cash price of his car?
Given: R = 16,200
t = 5 years
i(12)
= 10.5% = 0.105
m = 12
j = = 0.00875
n = mt = (12)(5) = 60

16. Find: P
P= R [1-( 1 + j)-n
]
j
= 16,200 [1-( 1 + 0.00875)-60
]
0.00875
P = 753,702.20 or 753,702
Cash Value= DP+P
= ₱200,000 + 753,702.20
= ₱953,702.20

17. Example 2. Suppose Mrs. Remoto would like to
save ₱3000 at the end of each month, for six
months, in a fund that gives 9% compounded
monthly. How much is the present value of her
savings after 6 months?
Example 3. The buyer of house and lot pays
₱200,000 cash and ₱10,000 at the end of each
month for 20 years. If money 9% compounded
quarterly, how much is the cash value of the car?
17,536.79 or 17,537
369,497.81 or 369,498 CV = 569,497

18. Future
Value of
General
Annuity

19. Future Value of General Annuity
F = R ( 1 + j)n
– 1 j = (1+-1
j
Where: R= Regular payments
n = total no. of payments
j = Equivalent rate per conversion period.
n = (m1)(t)
M1= payment interval
M2- length of compounding period.

20. Example 1: Mel started to deposit ₱1,000
monthly in a fund that pays 6% compounded
quarterly. How much will be in the fund after
15 years?
Given:
R=₱1,000;
r(m
2
)
=6% or 0.06
m1=12
m2=4
t= 15
n=(12)(15) = 180

21. Solution: j= (1+-1
j= (1+-1
j=
Finding F:
F=
=
F= ₱290,082.51

22. Example 2: Find the future value of an annuity of
=₱10,000.00 payable quarterly for 3 years if money
is worth 12% compounded monthly.
Example 3: Mrs. Santos is paying ₱11,400 monthly
for 2 years compounded semi-annually at a rate of
7%.
Example 4: ABC bank pays interest at the rate of 2%
compounded quarterly. How much will have in the
bank at the end of 5 years if you deposit ₱3,000
every month?