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Explicitly Stated (Posted on 2004-08-18) Difficulty: 3 of 5
A certain bank doesn't believe in interest and gives none the whole year. However, they do two things as a gift at the end of the year. They put money into your account such that it has 5 times as much as it did before. Then, they put 8 dollars in the account after that.

Jack gets one of these accounts at the start of year 1, and puts in 6 dollars. Assuming there are no other withdrawals or deposits into that account, figure out how much money is in that account at the beginning of year x, even if you don't know how much was in the account any of the previous years.

For example, on the beginning of year 1, he would have 6 dollars. On the beginning of year 2, he would have 38 dollars, and on the beginning of year 3 he would have 198 dollars.

What if you put in A dollars to start at the beginning of the first year, the bank put money into your account at the end of the year such that it was B times as much as before, and then put in C more dollars after that; how much money would you have at the beginning of year x, assuming everything else is normal and there are no withdrawals or deposits, even if you don't know how much was in the account any of the previous years?

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Solution Solution | Comment 3 of 11 |
Formula for sum of money in account at beginning of year x is:
For year 1, sum = A
For x>1, sum = (B^[x-1])*A + C*(B^0 + B^1 + B^2 + ..... + B^[x-2])
The following program verifies the formula.
Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Dim strgoagain As String
        strgoagain = "y"
        While strgoagain = "y"
            Console.WriteLine("Again ? (y/n)")
            strgoagain = LCase(Console.ReadLine()) '
        End While
    End Sub

    Sub mainline()
        Dim dbla As Double
        Dim dbla2 As Double
        Dim dblb As Double
        Dim dblc As Double
        Dim intyears As Integer
        Dim dblaccum As Double
        Dim dblformula As Double
        dbla = 0
        While dbla <= 0
            Console.WriteLine("What is the beginning sum ?")
            dbla = Int(Console.ReadLine())
        End While
        dbla2 = dbla
        dblb = 0
        While dblb <= 0
            Console.WriteLine("What is the multiplication factor?")
            dblb = Int(Console.ReadLine())
        End While
        dblc = 0
        While dblc <= 0
            Console.WriteLine("What is the year-end bonus?")
            dblc = Int(Console.ReadLine())
        End While
        intyears = 0
        While intyears <= 0
            Console.WriteLine("How many years should I verify?")
            intyears = Int(Console.ReadLine())
        End While
        For index1 As Integer = 1 To intyears
            computebyaccum(index1, dbla, dblb, dblc, dblaccum)
            computebyformula(index1, dbla2, dblb, dblc, dblformula)
            Console.WriteLine("After year " & Str(index1) & ":")
            Console.WriteLine("By accumulation: " & Str(dblaccum))
            Console.WriteLine("By formula: " & Str(dblformula))
            Console.WriteLine("Please press ENTER to continue.")
    End Sub

    Sub computebyaccum(ByRef intyear, ByRef dbla, ByRef dblb, _
    ByRef dblc, ByRef dblaccum)
        If intyear = 1 Then
            dblaccum = dbla
            dblaccum = _
            (dblb * dbla) + dblc
            dbla = dblaccum
        End If
    End Sub
Sub computebyformula(ByRef intyear, ByRef dbla2, ByRef dblb, _
    ByRef dblc, ByRef dblformula)
        Dim dblwork As Double
        If intyear = 1 Then
            dblformula = dbla2
            dblformula = (dblb ^ (intyear - 1)) * dbla2
            dblwork = 0
            For index1 As Integer = 0 To intyear - 2
                dblwork += dblb ^ index1
            dblwork *= dblc
            dblformula += dblwork
        End If
    End Sub
End Module

Edited on August 18, 2004, 11:51 am
  Posted by Penny on 2004-08-18 11:03:43

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