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ICSE Class 10 Answered

Amit deposited Rs. 150 per month in a bank for 8 months under the Recurring deposit scheme. What will be the maturity value of his deposits, if the rate of interest is 8% p.a and interest is calculated at the end of every month  
Asked by cyktron2 | 25 Jan, 2019, 06:41: PM
answered-by-expert Expert Answer
In a recurring deposit, interest is calculated every month means we need to calculate compound interest compounded every month.
 
deposit amount every month = Rs.150
rate of interest = 8% per annum
hence amount after 8 months = begin mathsize 12px style 150 cross times open parentheses 1 plus 8 over 1200 close parentheses to the power of 8 plus 150 cross times open parentheses 1 plus 8 over 1200 close parentheses to the power of 7 plus 150 cross times open parentheses 1 plus 8 over 1200 close parentheses to the power of 6 plus............... plus 150 cross times open parentheses 1 plus 8 over 1200 close parentheses squared plus 150 cross times open parentheses 1 plus 8 over 1200 close parentheses end style
Let us use the approximation (1+x)n = 1+nx  if  x<<1.
 
Then Amount = begin mathsize 12px style 150 cross times open square brackets open parentheses 1 plus 8 cross times 2 over 300 close parentheses plus open parentheses 1 plus 7 cross times 2 over 300 close parentheses plus open parentheses 1 plus 6 cross times 2 over 300 close parentheses plus.................... open parentheses 1 plus 2 cross times 2 over 300 close parentheses plus open parentheses 1 plus 2 over 300 close parentheses close square brackets end style
Amount = 150×[ 8 + (2/300)(8+7+6.........+2+1) ]  = 150×[8+(2/300)(8×9/2)] = 150×8.24 = Rs.1236
Answered by Thiyagarajan K | 26 Jan, 2019, 08:06: AM
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