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Interest on a bank deposit
 Yn = Y0(1+r)n
Can solve for any variable, as long as we know the other three.
Example of solving for the ending balance. Suppose that:
ending balance, Y4 = $1464.10
In a spreadsheet, such as Microsoft Excel, you use the formula +1000*(1+.10)^4
Next example--Solve for beginning balance. Same example as before, except we want to know how much to deposit now in order to have $1600 in four years.
1600 = Y0(1+0.10)4
Divide 1600 by (1.1)4 to get $1092.82
Next example--Solve for interest rate. Suppose you start with $1000 and end up with $1600 after four years. What was the interest rate?
1600 = 1000(1+r)4
Final example--Solving for the number of years. Suppose you start with $1000, the interest rate is 10 percent, and you want to know how long it will take until you have $2000. Here, we use logs (you can use either regular logs or natural logs).
logYt = logY0 + t[log(1+r)]
Solving for t gives
t = (logYt - logY0)/log(1+r)
In our example
t = (log - log)/log[1+.10] = 7.27 years
For problem set, note that:
In general, a ratio increases when the numerator grows faster than the denominator, and vice-versa.