16. A person has deposited `25,000 in an investment which yields 14% simple interest
annually. Do these amounts (principal + interest) form an A.P.? If so, determine the
amount of investment after 20 years.
Answers
Principal (P) = 25000, Rate(R) = 14%, T = 1 year
Simple interest(S.I) = P×T×R/100
S.I = (25000 x 1 x 14)/100
S.I = 250 × 14
S.I= 3500
Amount = principal + interest
A = P + I
A = 25000 + 3500
A = 28500
Amount at the end of the Ist year = 28500
Amount at the end of 2nd year = 28500 + 3500
Amount at the end of 2nd year= 32000
Amount at the end of third year = 32000 + 3500
Amount at the end of third year= 35500
28500,32000,35500.,… Which forms an arithmetic sequence (AP).
In this question we need to find 20th term
tn = a +(n - 1) d
Here,a = 28500, d = 32000 – 28500 = 3500
t20 = 28500 + (20 - 1) 3500
t20 = 28500 + 19 (3500)
t20 = 28500 + 66500
t20= 95000
Hence, the amount of investment after 20 years is 95,000
HOPE THIS WILL HELP YOU..
Solution :
i ) Principal ( P ) = Rs 25000
Simple interest = 15% of 25000
S.I = ( 15/100 ) × 25000
S.I = Rs3500
ii ) Amount ( A ) = P + S.I
A = Rs 25000 + Rs 3500
A = Rs28500
Therefore ,
At the end of the first year
Amount of the investment Rs28500
ii ) End of the second year
Amount = Rs28500+S.I
= 28500+3500
= Rs32000
iii ) Amount of the investment
at the end of 3rd year
= Rs 32000 + Rs 3500
= Rs 35500
iv ) Now , arranging the amounts
yearwise ,
28500, 32000,35500, ...it is
clearly in A.P
First term = a = a1 = 28500,
common difference = d
d = a2 - a1
d = 32000 - 28500
d = 3500
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nth term in A.P = an
an = a + ( n - 1 )d
************************************
Here ,
n = 20,
a20 = 28500 + ( 20 - 1 )( 3500 )
= 28500 + 19 × 3500
= 28500 + 66500
= 95000
Therefore ,
The amount of investment after
20years = Rs 95000
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