Mathematics of Investment: Simple Annuity Due

investment

1. SIMPLE ANNUITY DUE
MATH 106 Mathematics of Investment

2. ANNUITY DUE
Annuity due is a type of annuity where the payments are made at the
beginning of each payment interval, unlike ordinary simple annuity the
apyment interval starts at the end of each period.
For example, when equipment or property is leased, the regular lease
payments are usually paid in advance.
Another example, in educational plan wherein you need to pay it in
advance regular period with fixed amount.
In these cases, the topic is restricted to simple annuity situations, in
which compounding interval equals the payment interval.

3. S = R [ - 1]
due(1+i) - 1
(n+1)i
FUTURE VALUE
(1-n)
A = R [ +1]
due1 - (1 + i)
i
PRESENT VALUE
SIMPLE ANNUITY FORMULA
where:
R = Size of each annuity payment
j = Nominal interest rate
m = Number of conversion per year
t = Time period (term) of the loan or investment
n = Number of payments in the annuity
i = Interest rate per compounding period

4. Example 1
Jesreal Eismar Fernando made deposits of P900 at the beginning of each
month to WSS Cooperative, which pays 12 % compouned monthly. After 4
years, Jesreal Eismar makes no more deposits. Whta will be the balance in
the account 7 yeaars after the last deposit?

5. Example1

6. Assignment (1)
How much will Small Laude accumulate in her insurange policy by age 60 if
the first semiannual contribution of P10,000 is made on her 28th birthday and
the last is made six months before her birthday? Assume that her insurance
policy earns 11% compounded semiannually.

7. Solution1
1
2

8. Example 2
MS Services Acquired computers under a capital lease agreement. MS
Services pays the lessor P300,000 per year at the beginning of each year for
six years. If MS can obtain six-year financing at 10% compounded annually,
what is the long-term, lease liability will MS report in its financial statements?

9. Example2

10. Assignment (2)
Shiela’s furniture is advertising a Lazy Boy Chair for P5,000 down monthly
payments of P5,000, including interest at 18% compounded monthly. What is
the cash price of the chair?

11. Solution2
1
2

12. Any Questions?