Question

25. A sum was borrowed at 20% p.a. compound interest
It was repaid in three annual installments at the end
of one year, two years and three years respectively.
The first, second and third installments were 2400,
2304 and 5184 respectively. Find the sum
borrowed (in ).​

Answer 1

Given : A sum was borrowed at 20% p.a. compound interest.

It was repaid in three annual inst alments with each inst alment being paid at the end of an year.

The first, second and third inst alments were  2400,  2304 and  5184 respectively.

To Find : the sum

Solution:

Let say sum was   100P  

SI = P * R * T/100  with in compounding period , SI = CI

Interest for first year  = 100P * 20 * 1 /100  = 20P

First Inst allment = 2400

Hence Amount left to be paid  = 100P + 20P  - 2400

= 120P - 2400

= 120(P - 20)

Interest for second year   =120(P - 20) * 20 * 1 /100  

= 24(P - 20)

Second Inst allment = 2304

Amount left to be paid  = 120(P - 20) + 24(P - 20)  -2304

= 144(P - 20) - 2304

= 144(P - 36)

Interest in 3rd year = 144(P -36) * 20 * 1 /100

=  144(P - 36)  ( 1/5)

Total Amount to be paid   = 144(P - 36) +  144(P - 36)  ( 1/5)

= 144(P - 36)  ( 6/5)

Amount paid in 3rd inst allment = 5184

144(P - 36)  ( 6/5)   = 5184

=> P - 36 = 30

=> P = 66

=> 100P  = 6600

Sum was Rs  6600

Verification

Initial Amount   Interest           Inst allment    Left

6600                 1320                 2400            5520

5520                1104                   2304            4320

4320                 864                   5184             0

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