`Mr. Shariq owes Mr. Farooq Rs. 7000 due in 5 years and Rs. 15,000 in 7 ½ years. How much should Mr. Shariq pay at the end of 6 years which may be acceptable to Mr. Farooq if money is worth 8% compounded semi-annually?
Answers
Given : Mr. Shariq owes Mr. Farooq Rs. 7000 due in 5 years and Rs. 15,000 in 7 ½ years. money is worth 8% compounded semi-annually
To find : How much should Mr. Shariq pay at the end of 6 years which may be acceptable to Mr. Farooq
Solution:
R = 8 % per annum = 4% half yearly
Let say Present debt is x for debt Rs 7000/ due 5 years hence
Hence 7000 = x( 1 + 4/100)¹⁰
=> 7000 = x ( 1.04)¹⁰
=> x = 7000 (1.04)⁻¹⁰
Let say Present debt is y for debt Rs 15000/ due 7 ½ years hence
Hence 15000 = y( 1 + 4/100)¹⁵
=> y = 15000 ( 1.08)⁻¹⁵
Total debt at present = 7000 (1.04)⁻¹⁰ + 15000 ( 1.08)⁻¹⁵
To be paid 6 years Hence = A
A = ( 7000 (1.04)⁻¹⁰ + 15000 ( 1.08)⁻¹⁵ ) ( 1 + 4/100)¹²
=> A = ( 7000 (1.04)⁻¹⁰ + 15000 ( 1.08)⁻¹⁵ ) ( 1.04)¹²
=> A = 7000 (1.04)² + 15000 ( 1.04)⁻³
=> A = 7,571.2 + 13,334.9
=> A = 20,906.1
Payment = Rs 20,906.1
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