Page 39 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Personal Financial Planning

Notes 2.9.2 Present Value of Annuity Due

PVA = CIF (FVIF ) (1 + I) or
n I . n
⎛ 1 − (1 I ) − n ⎞
+
PVA = CIF ( + ) I
1
n ⎜ ⎟
⎝ I ⎠
Illustration 26
Mr. Bhat has to receive ` 500 at the beginning of each year, for 4 years. Calculate personal value
of annuity due, assuming 10 per cent rate of interest.

Solution:
PVA = ` 500 (3.170)× (1.10) = ` 1743.5
4
Alternatively

Years Cash inflow (`) PV Factor at 10 per cent Present value (`)
1 500 1.00 500.0
2 500 0.909 454.5
3 500 0.826 413.0
4 500 0.751 375.5
PV of Annuity 1743.0

2.10 Effective vs Nominal Rate

The nominal rate of interest or rate of interest per year is equal. Effective and nominal rate are
equal only when the compounding is done yearly once, but there will be a difference, that is,
effective rate is greater than the nominal rate for shorter compounding periods. Effective rate of
interest can be calculated with the following formula.
⎛ I ⎞ m
ERI = ⎜ 1 + ⎟ − 1
⎝ m ⎠
Where,

I = Nominal rate of interest.
m = Frequency of compounding per year.
Illustration 27
Mr. X deposited ` 1000 in a bank at 10 per cent of the rate of interest with quarterly compounding.
He wants to know the effective rate of interest.
Solution:

⎛ 0.10 ⎞ 4
ERI = ⎜ 1 + ⎟ − 1
⎝ 4 ⎠
= 1.1038 – 1 = 0.1038 or 10.38 per cent.

2.11 Sinking Fund Factor

The financial manager may need to estimate the amount of annual payments so as to accumulate
a predetermined amount after a future date, to purchase assets or to pay a liability. The following
formula is useful to calculate the annual payment.

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