A house is sold for Rs. 500000 down and 10 semi-annual payments of Rs. 50000 each, the first due 3 years hence. Find the cash price of the house if money is worth 20% compounded semi-annually.
Answers
Given : A house is sold for Rs. 500000 down and 10 semi-annual payments of Rs. 50000 each, the first due 3 years hence.
To Find : the cash price of the house if money is worth 20% compounded semi-annually.
Solution:
EMI Formula = [P x (R/100) x (1+(R/100))ⁿ]/[(1+(R/100))ⁿ-1]
R = 10 % for half year
n = 10 half years
EMI = 50000
=> 50000 = [P x (10/100) x (1+(10/100))¹⁰]/[(1+(10/100))¹⁰-1]
=> 500000 = P (1.1)¹⁰ / ( (1.1)¹⁰ - 1)
=> P = 3,07,228.355
But this P is after 2.5 years as first due 3 years hence
Amount at at time of purchase = 3,07,228.355 /( 1 + 10/100)⁵
= 1,90,764.64
cash price of the house = 500000 + 1,90,764.64
= 6,90,764.64 Rs
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