At the end of t years the future value of an investment of 6

At the end of t years, the future value of an investment of $6000 in an account that pays 9% APR compounded monthly is S = 6000 (1 + 0.09/12)^12t dollars. Assuming no withdrawals or additional deposits, how long will it take for the investment to reach $18,000? Round to three decimal places. The sales of a new model of notebook computer are approximated by S(x) = 5000 - 12,000e^-x/9, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $1, 500,000?

Solution

S = 6000[1 + 0.09/12]^12t

=> 18,000 = 6000[1 + 0.09/12]^12t

=> 3000 = [1.0075]^12t

taking ln on both sides, we get:

ln(3000) = 12t ln(1.0075)

=> t = 89.3 years.

43] S = 5000 - 12000e^-x/9

1,500 = 5,000 - 12000e^-x/9

[S = 1,500,000/1000 = 1500 since S is in thousands]

=> 3500 = 12000e^-x/9

=> 0.29167 = e^-x/9

taking ln on both sides we get:

1.232 = x/9

=> x = 11.1 or x = 11 months.