4.3 Ordinary and Simple Annuity

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5.3 ANNUITY
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5.3 Ordinary and Simple Annuity

• Define ordinary and simple annuity
• Find the future and present value
• Find the regular periodic payment
• Find the interest

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If we wish to invest in Amanah Saham Bumiputera
with a fixed installment of RM100 monthly. If the
scheme gives 10 interest monthly, try and
calculate the amount accumulated after 10 years.
At the end of the first month, we will have
100(0.1) 100 RM A At the end of the second
month, we will have A (0.1) 100 RM B At the
end of the third month, we will have B (0.1)
100 RM C
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Definition - Annuity

• An annuity is a sequence of equal payments made
  at equal intervals of time.
• The payments are computed by the compound
  interest method such as annually, semiannually,
  quarterly or monthly.
• Assume that the first payment is made at the end
  of the first interest period.
• Annuities in which payments are made at the same
  time the interest is compounded are called
  ordinary and simple annuities.

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Future Value of an Ordinary Annuity
The future value of an annuity of R ringgit per
period for n period when the interest rate is i
per period is given by
Sn future value R regular or periodic
payment i interest rate per compounding
period n number of annuity payments
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Example 1 future value
Ali has made equal payments of RM100 every 6
months at an interest rate of 5 compounded
semiannually for 5 years. The future value which
is the amount he gets after 5 years is
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Example 2
Lim decides to save RM1000 per month in her
saving account that pays 8 interest p.a
compounded monthly. After making 8 deposits, how
much money does Lim have?
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Example 3
A teenager plans to deposit RM50 in a savings
account at the end of each quarter for the next 6
years. Interest is earned at a rate of 8 percent
per year-compounded quarterly. What should her
account balance be 6 years from now? How much
interest will she earn?
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Example 4 Finding saving amount to achieve future
goal
Suppose you want to buy a house 5 years from now
and you want to estimate that an initial down
payment of RM20,000 will be required at that
time. Suppose a saving account paying annual
interest rate of 6 p.a compounded annually. How
much do you need to make equal annual end-of-year
deposit into the saving acount to accumulate the
RM20,000 at the end of year 5?
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Present value of an Ordinary Annuity
The present value of an ordinary annuity of R
Ringgit per period for n period when the rate of
return or interest is i per period is given by
An present value R regular or periodic
payment i interest rate per compounding
period n number of annuity payments
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Example 5 Finding present value
Find the present value which is the amount to be
invested now in order to receive equal payments
of RM100 every 6 months for 5 years.
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Example 6 Finding the amount of payment of a
loan
Lim plans to start up a new business and he
needs to borrow RM100,000. You propose to pay off
the loan quickly by making 5 equal annual
payments. If the interest rate is 10p.a
compounded annually, how much is the amount of
each payment?
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Example 7 Finding loan amount and interest paid
Veni agrees to pay RM 300 per month for 48
months to pay off a car loan. If interest of 12
per annum is charged monthly, find a) how much
did the car originally cost? b) how much
interest was paid?
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Example 8
Rudy buys a land for RM110,000. He makes 20 down
payment and the balance he takes a loan for 25
years that charges an annual interest rate of 5
compounded monthly. Find (a) the monthly
payments. (b) the total amount of interest that
will be paid. (c) the amount of the loan that
will have already paid after 10 years.
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b) Monthly payment of RM514.44 for 25 years yield
a total payment 514.44(25)(12) RM154,331.77
Thus the total amount of interest RM154,331.77-
88,000
RM66,331.77
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c)
An
72,444.94 The amount of loan that will have
already paid after 10 years is RM88,000-
RM72,444.94 RM15,555.05
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Example 9 Finding amount of annuity

• Hisham is 20 years away from retiring and starts
  saving RM100 a month in an account paying 6 p.a
  compounded monthly. When he retires, he wishes to
  withdraw a fixed amount each month for 25 years.
  What will the fixed amount be?

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Example 10
Mariam purchased a house by paying RM5,750.32
down and promised to pay RM811.41 every months
for next 15 years. The interest charged is at the
rate of 9 compounded monthly. a) What was
the cash value of the house? b) If Mariam missed
the first 10 payments, what must she pay at
the time the 11th payment is due to bring herself
up to date? c) After paying for the first 5
years, Mariam wished to discharge her
remaining debt by making single payment at
time when the 61st regular payment was due. What
must she pay in addition to the regular
payment then due?
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Example 11
At the end of every month, Mr. Zaki saves RM200
in an account that pays an annual rate of 10
compounded monthly. After 3 years, he adds RM60
to his savings per month. Show that the total
amount after 6 years is RM22,129.17
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