SOLUTION: An investor opens an account at a investment firm earning 6% interest (annual rate) with an initial deposit of $6000. Each month, the investor makes a deposit of $150, but the bank

Question 1042392: An investor opens an account at a investment firm earning 6% interest (annual rate) with an initial deposit of $6000. Each month, the investor makes a deposit of $150, but the bank charges a $10 fee.
Write a difference equation describing the balance at month n+1 given the balance at month n.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the annual percentage rate is 6%.
this is equal to an annual rate of .06.
divide this by 12 and you get a monthly rate of .06/12 = .005
the formula for each successive payment is derived as follows:
B.0 = 6000
B.1 = B.0 * 1.005 + 140
B.2 = B.1 * 1.005 + 140
B.3 = B.2 * 1.005 + 140
B.n = B.n-1 * 1.005 + 140
B.n+1 = B.n * 1.005 + 140

the . means sub, so B.n means B sub n, etc.

the amount invested in each period is multiplied by the monthly interest rate to get the amount invested in the next period.
then 150 deposit is added to this and 10 fee is subtracted from it to get a net monthly deposit of 140.

example:
you start with 6000 in time period 0.
this earns .005 interest in time period 1.
you have 6000 * 1.005 = 6030 in time period 1.
then you add 150 deposit to it and subtract 10 fee from it to get 6030 + 150 - 10 = 6170 in time period 1.
you now have 6170 in time period 1.
you multiply that by 1.005 to get 6200.85 in time period 2.
then you add 140 to it (150 - 10 = 140) to get a total of 6340.85 in time period 2.
you do the same for each time period.

after 9 periods, you should have a total investment of 7560.96

here are the detailed calculations using excel spreadsheet.

$$$

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