Asked by Frank
A bank account pays interest at 12% compounded monthly, and has a monthly fee of $10, deducted at the end of each month. If $13,000 is deposited on January 1, 2013, how much is in the account on January 1, 2016?
I have done some question related to compound interest however the fact that the montly fee is 10$ and not a percentage confuses me.
I have done some question related to compound interest however the fact that the montly fee is 10$ and not a percentage confuses me.
Answers
Answered by
Steve
Suppose the initial amount is x, the monthly rate is r=1.01, and the fee is f. Then the amount left at the end of each month is
x*r-f
(xr-f)*r-f = xr^2-fr-f
(xr^2-fr-f)*r-f = xr^3-fr^2-fr-f
The amount at the end of the nth month is thus
xr^n - f(r^n-1)/(r-1)
So, for your problem, the balance after 12 months will be
13000*1.01^12 - 10(1.01^12-1)/(1.01-1) = 14521.90
Had there been no fees deducted, the amount would have been
13000*1.01^12 = 14648.73
A flat $120 deducted at the end of the year would have left 14528.73
The deductions from the amount earning interest thus reduced the balance by $7 or so.
x*r-f
(xr-f)*r-f = xr^2-fr-f
(xr^2-fr-f)*r-f = xr^3-fr^2-fr-f
The amount at the end of the nth month is thus
xr^n - f(r^n-1)/(r-1)
So, for your problem, the balance after 12 months will be
13000*1.01^12 - 10(1.01^12-1)/(1.01-1) = 14521.90
Had there been no fees deducted, the amount would have been
13000*1.01^12 = 14648.73
A flat $120 deducted at the end of the year would have left 14528.73
The deductions from the amount earning interest thus reduced the balance by $7 or so.
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