Rajiv Bhardwaj has a recurring deposit account in a bank of 600 per month. If the bank pays simple interest of 7% p.a. and he gets 15450 as maturity amount, find the total time for which the account was held.
Answers
Answer
It is given that,
Amount deposited per month (P) = ₹ 600,
Rate of interest = 7% p.a.
Amount of maturity = ₹ 15,450.
Consider n months as the period,
We know that
Total principal for one month = 600∗n(n+1)/2
By further calculation,
= 600(n
2
+n)/2
= 300(n
2
/n)
Here interest = PRT/100,
Substituting the values
= (300(n
2
+1)∗7∗1)/(100/12)
= 7/4(n
2
+n)
Amount of maturity = 600n+7/4(n
2
+n),
Substituting the values
600n+7/4(n
2
+n)=15450
By further calculation
2400+7n
2
+7n=61800
7n
2
+2407n−61800=0
We can write it as,
7n
2
−168n+2575n−61800=0
7n(n−24)+2575(n−24)=0
(n−24)(7n+2575)=0
Here, n−24=0 where n=24
Similarly
7n+2575=0
Where 7n=−2575
n=−2575/7 which is not possible as it is negative.
Period (n) = 24 months or 2 years.