Q1. Mrs Ranjana deposits 1600 per month in a recurring
deposit account at 9% p.a. S.I. If she gets Rs. 65592
at the time of maturity, find the total time for which
the account was held.
(Time in months)
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Answers
Answer:
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Step-by-step explanation:
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The account was held for 36 months.
Step-by-step explanation:
Given:
monthly deposit= Rs.1600
rate of interest= 9% p.a.
Amount received= Rs 65592
To find:
time period
Solution:
Let m be the number of months to find
Now as we know, N= m(m+1)
2 X 12
According to the formula for simple interest,
Principal amount= Pm + PNR/100
But the principal amount is already given
65592= 1600 (m)+ 1600 X m(m+1) X 9
2 X 12 X 100
65592= 1600m+ 800 X m(m+1) X 3
1 X 4 X 100
65592= 1600m+ 8 X m(m+1) X 3
1 X 4 X 1
65592= 1600m+ 2 X m(m+1) X 3
1 X 1 X 1
65592= 1600m+ 6 X m(m+1)
65592= 1600m+ 6 X (m²+m)
65592= 1600m+ 6m²+6m
adding the like terms
65592 = 1606m+ 6m²
Now, 6m²+1606m-65592=0
Using the factrization method
6m²+ 1822m-36m-65592=0
Taking out the like terms
m(6m+1822)-36(6m+1822)=0
(6m+1822) (m-36)=0
(6m+1822)=0 or (m-36)=0
6m+1822=0 or m-36=0
6m = -1822 or m= 36
m= -1822/6 or m= 36
But the answer cannot be negative
Hence, m=36 will be correct
The account was held for 36 months that is 3 years
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