Beginner
1. Consecutive Prime Sum2. Alpha Numeric Sorting3. Longest Progressive Sequence4. Divine Divisor5. Forest Fire6. Minimum Distance7. Saving for a rainy day8. Online Communities Even Groups9. Coin Distribution10. Bank Compare11. Counting Rock Samples12. Collecting Candies13. Game Of Primes14. Kth Largest Factor15. Jumble With Numbers16. Philand Coins17. Reverse Gear18. String Rotation19. The Vita Sum20. Mountain Peak Sequence21. LAZY STUDENT22. LOGIC PYRAMID23. Super ASCII String Checker24. Min Product Array25. String Of Brackets26. Exchange Of Digits27. Marathon Winner28. Common Steps29. Swayamvar30. Digit Pairs31. Dole Out Cadbury32. Petrol Pump33. Grooving Monkeys34. Death BattleSaving for a rainy day
LEVEL:Beginner
Description
By nature, an average Indian believes in saving money. Some reports suggest that an average Indian manages to save approximately 30+% of his salary. Dhaniram is one such hard working fellow. With a view of future expenses, Dhaniram resolves to save a certain amount in order to meet his cash flow demands in the future.
Consider the following example.
Dhaniram wants to buy a TV. He needs to pay Rs 2000/- per month for 12 installments to own the TV. If let's say he gets 4% interest per annum on his savings bank account, then Dhaniram will need to deposit a certain amount in the bank today, such that he is able to withdraw Rs 2000/- per month for the next 12 months without requiring any additional deposits throughout.
Your task is to find out how much Dhaniram should deposit today so that he gets assured cash flows for a fixed period in the future, given the rate of interest at which his money will grow during this period.
Input Format
First line contains desired cash flow M
Second line contains period in months denoted by T
Third line contains rate per annum R expressed in percentage at which deposited amount will grow
Constraints:
M > 0
T > 0
R >= 0
Calculation should be done upto 11-digit precision
Output Format
Print total amount of money to be deposited now rounded off to the nearest integer.
500 3 12
1470
6000 3 5.9
17824
500 2 0
1000
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Approach
To get the question correctly lets take the first example which is
500 3 12
output is 1470
for first month: 1470 * (1/12) * (12/100) = 14.7 rounded to 15
1470 + 15 = 1485
above we have added 12/100 because for a year there are 12 months and percentage is calculated per 100 so 12/100 and we have 1/12 because 12 percent is calculated per year , then for one month it would be 1/12 of 12 percent which is (1/12) * (12/100)
after first month withdrawal 1485-500 = 985
for second month: 985 * (1/12) * (12/100) = 9.85 rounded to 10
985+10 = 995
after second month withdrawal 995 - 500 = 495
for third month 495*(1/12)*(12*100) = 4.95 rounded to 5
495+5 = 500
which is sufficient for the third month withdrawal
required amount = present amount + present amount * (interest %/ deposited period)
deposited period = 1/12 (for calculating the interest gained for per month)
interest % = interest/100
present amount = required amount/(1 + interest % / deposited period )
present amount = required amount/ (1 + interest % / 1200)
to find interest amount from present amount
interest = required amount- present amount
required amount = required amount + ( monthly pay- interest)
so our final logic will be
repeat month time {
present amount = required amount / (1+interest% / 12)
interest = required amount- present amount
required amount = required amount -(monthly pay-interest)
}
Note :
Let us know if you can come up with a better approach, mail us at support@theinquisitive.in Your approach will be reviewed and posted with credits to you.
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