How much amount is required to be invested every year so as to accumulate Rs. 300000 at the end of
10 years if interest is compounded annually at 10%?
Answers
Given : Amount invested every year so as to accumulate Rs. 300000 at the end of 10 years if interest is compounded annually at 10
To Find : amount invested
Solution:
A = P(1 + R/100)ⁿ
Amount Invested every Year = P
Amount invested at beginning of 1st Year will become = P(1 + R/100)¹⁰ after 10 years
Amount invested at beginning of 2nd Year will become = P(1 + R/100)⁹ after 10 years
Total amount = P(1 + R/100)¹⁰ + P(1 + R/100)⁹ + . + P(1 + R/100)² + P(1 + R/100)
This is an GP
a = P(1 + R/100)
r = (1 + R/100)
n = 10
Sₙ = a(rⁿ - 1)/( r - 1)
= P(1 + R/100) ((1 + R/100)¹⁰ - 1) / ( 1 + R/100 - 1 )
= P((100 + R)/100) ((1 + R/100)¹⁰ - 1) / ( R/100)
= P((100 + R)) ((1 + R/100)¹⁰ - 1) /R
R = 10
300000 = P((100 + 10)) ((1 + 10/100)¹⁰ - 1) /10
=> 300000 =11P ( 1.1¹⁰ - 1)
=> P = 300000/ 11 ( 1.1¹⁰ - 1)
=> P = 17,112.38
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