Tips on Solving Problems Based on Simple & Compound Interest

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3 TIPS on cracking Aptitude Questions on Simple
and Compound Interest
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Tip 1 Understand the formulae
Amount to be repaid after N years if simple
interest is applied P (P x N x R) P (1 N
x R) Simple Interest P x N x R Amount to be
repaid after N years if interest is compounded
P (1 R)N Compound Interest P x (1
R)N - P

• Question Simple interest on a certain sum of
  money for 3 years at 8 per annum is half the
  compound interest on Rs. 4000 for 2 years at 10
  per annum. Calculate the principal placed on
  simple interest.
• Solution
• Let the Principal be Rs. P.
• Then, SI (P x R x T) 0.24P
• Given CI 4000(1 0.1)2 4000 4000(1.21 1)
  4000 x 0.21
• According to the question,
• 0.24P 2000 x 0.21
• P 2000 x 0.21 / 0.24 2000 x 7 / 8 Rs. 1750

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Tip 2 If the interest rate is applied on a
half-yearly, quarterly or monthly basis, the
effective annual rate is calculated by
compounding the interest.

• Question What is the effective annual rate of
  interest corresponding to a nominal rate of 6
  per annum payable half-yearly?
• Solution
• Let the Principal be Rs. P.
• Now, the rate is 6 per annum but the interest
  has to be paid twice a year (i.e.) an interest of
  3 is applied every 6 months.
• Amount to be repaid after 1 year P x 1.03 x
  1.03 1.0609P
• Effective Annual Rate of interest 6.09

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Tip 3 Use logarithms to find the time when
compound rates are applied

• log 2 0.301 log 4 0.602 log 6 0.778
• log 3 0.477 log 5 0.699 log 7 0.845
• Question At 3 annual interest compounded
  monthly, how long will it take to double your
  money?
• Solution
• Let the number of months be n and the Principal
  be Rs. P.
• Then, P(1 0.03)n 2P
• (1 0.03)n 2
• n log ( 1.03) log 2
• n log 2 / log 1.03 0.301 / 0.128 23.5
• Thus. Itll take 1 year and 11.5 months.

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  Questions on Simple Compound Interest.