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Question
Ankita started paying Rs 400 per month in a 3 years recurring deposit. After six months her brother Anshul started paying Rs 500 per month in a `2(1)/(2)` years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?
Solution
In case of Ankita,
Deposit per month = Rs 400
Period(n) = 3 years = 36 months
Rate of interest = 10%
Total principal for one month
= `400 xx ("n"("n" + 1))/(2)`
= `400 xx (36(36 + 1))/(2)`
= `₹(400 xx 36 xx 37)/(2)`
= ₹266400
Interset
= `"prt"/(100)`
= `(266400 xx 10 xx 1)/(100 xx 12)`
= ₹2220
∴ Amount of maturity
= ₹400 x 36 + ₹2220
= ₹14400 + ₹2220
= ₹16620
In case of Anshul,
Deposit P.m. = ₹500
Rate of interest = 10%
Period(n) = `2(1)/(2)` year = 30months
∴ Total principal for one month
= `₹500 xx ("n"("n" + 1))/(2)`
= `500 xx (30(30 + 1))/(2)`
= `₹(500 xx 30 xx 31)/(2)`
= ₹232500
Interest
= `(232500 xx 10 xx 1)/(100 xx 12)`
= ₹1937.50
Amount of maturity
= ₹500 x 30 + ₹1937.50
= ₹15000 + ₹1937.50
= ₹16937.50
At maturity Anshul will get more amount
DIfference
= ₹16937.50 - ₹16620.00
= ₹317.50.
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