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**Note**Course:
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Placement Preparation
**Specialization:
**Quantitative Aptitude**Offline Downloads:
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Compound Interest
Invest €500 that earns 10% interest each year for 3 years,
where each interest payment is reinvested at the same rate:
End of
interest earned
amount at end of period
Year 1
50
550 = 500(1.1)
Year 2
55
605 = 500(1.1)(1.1)
Year 3
60.5
665.5 = 500(1.1)3
The interest earned grows, because the amount of money it is
applied to grows with each payment of interest. We earn not only
interest, but interest on the interest already paid. This is called
compound interest.
More generally, we invest the principal, P, at an interest rate r for a
number of periods, n, and receive a final sum, S, at the end of the
investment horizon.
S = P(1 + r )
n

Example:
A principal of €25000 is invested at 12% interest compounded
annually. After how many years will it have exceeded €250000?
10 P = P (1 + r )
n
Compounding can take place several times in a year, e.g. quarterly,
monthly, weekly, continuously. This does not mean that the quoted
interest rate is paid out that number of times a year!
Assume the €500 is invested for 3 years, at 10%, but now we
compound quarterly:
Quarter
interest earned
amount at end of quarter
1
12.5
512.5
2
12.8125
525.3125
3
13.1328
538.445
4
13.4611
551.91
Generally:
r⎞
⎛
S = P ⎜1 + ⎟
⎝ m⎠
nm

where m is the amount of compounding per period n.
Example:
€10 invested at 12% interest for one year. Future value if
compounded:
a) annuallyb) semi-annuallyc) quarterly
d) monthly e) weekly
As the interval of compounding shrinks, i.e. it becomes more
frequent, the interest earned grows. However, the increases
become smaller as we increase the frequency. As compounding
increases to continuous compounding our formula converges to:
S = Pe rt
Example:
A principal of €10000 is invested at one of the following banks:
a) at 4.75% interest, compounded annually
b) at 4.7% interest, compounded semi-annually
c) at 4.65% interest, compounded quarterly
d) at 4.6% interest, compounded continuously

=>
a) 10000(1.0475)
b) 10000(1+0.047/2)2
c) 10000(1+0.0465)4
d) 10000e0.046t

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