A red wine’s value depends on the length of time it is aged in oak casks before it is bottled. If the relationship between the value of the wine and its length of time in oak casks is given by
Value in terms of today’s dollars = $(10 + 5 ln( t + 1)), where t is measured in years.
To the nearest tenth of a year, how long will the wine be aged if the interest rate is 4%?
To the nearest tenth of a year, how long will the wine be aged if the interest rate is 2.52%?
Is the interest rate in this problem a “real” or “nominal” interest rate? Explain.
Though you can do this problem with pencil and paper and a calculator, it may be easiest to do it in a spreadsheet. Though not necessary, the first derivative of the value with respect to t (i.e., the slope of the value line at any single point) is = 5/(t+1).