Question

An amount of rs. 12820 due 3 years hence, is fully repaid in three annual installments staring 1 year. the first installment is 1/2 the second installment and the second installment is 2/3 of the third installment. if the rate of interest is 10% per annum, find the first installment.​

Answer 1

Answer:

2662

Step-by-step explanation:

Let say Third installments =  3T   Rs

Second installment = (2/3)3T  =  2T   Rs

First Installment =  (1/2)2T  = T   Rs

Total installments = 3T + 2T + T = 6T

Interest Amount for 1st Year = 12820 * 10 /100  = Rs 1282

Principle for 2nd year = 12820 + 1282 - T = 14102 - T   Rs

Interest Amount for 2nd Year  (14102 - T ) *10/100  =  1410.2  - 0.1T  Rs

Principle for 3rd Year = 14102 - T +  1410.2  - 0.1T - 2T  = 15512.2 - 3.1T   Rs

Interest for 3rd Year =  (15512.2 - 3.1T)*10/100 = 1551.22 - 0.31T  Rs

Total Amount to be Paid = 12820 + 1282 +  1410.2  - 0.1T + 1551.22 - 0.31T

= 17063.42 - 0.41T

=> 17063.42 - 0.41T = 6T

=> 17063.42 = 6.41T

=> T = 2662

First Installment = T = Rs 2662