A man saves Rs $200$ at the end of each year and lends this saving at $5\%$ compound interest. How much will it worth at the end of $3$ years?
This is a simple problem indeed and we got through text book Combined Defence Services Exam (Jain & Kishore) - question 1
Answer provided is in the book is $662.02$
Step given is $200(1+5/100)^3+200(1+5/100)^2+200(1+5/100)^1=662.02$
But I got my doubts in this, the savings are at year end, so the $200$ deposited after first year will be $200(1+5/100)^2$ after end of three years because the duration is two years only (from first year end to third year end). Like that other parts also.
While searching in internet, we got these other sources also
Answer: $662.02$ (as available in Upkar's Cds Mathmatics, question 27)
Answer: $662.02$ (as available in sscadda.com)
Answer: $630.50$ (as available in careerbless.com)
Therefore, almost all votes goes for $662.02$ except for the last site. But I guess the last site is correct because, from first year end to third year end, duration is 2 year. likewise, from second year end to third year end, duration is 1 year.
Please help me to chose the right solution. (for my exam, I don't need to take any chance and hence posted here to clarify) thanks
This is a matter of interpretating the language in the question. It isn't about the mathematics at all. The intent of the first 3 sources is that the "3 years" starts with his first investment of the Rs 200 that he had earned the year before. The final source interpreted it as you did: the "3 years" begins with no money, and the man has to wait the first year to earn anything to invest.
In my opinion, the way the question is stated points more towards your interpretation than the other. However, I can see how it could be taken either way. It's just a poorly worded question.