Consider an investment of $6000 that earns 4.5% interest. How long would it take for the investment to reach 1500 if the interest is compounded monthly?

Respuesta :

Answer:

  20.4 years

Step-by-step explanation:

The future value formula is ...

  FV = P(1 +r/n)^(nt)

where P is the principal invested (6000), n is the number of times per year compounding occurs (12), r is the interest rate (.045), and t is the number of years.

Perhaps you're interested in a future value of $15,000 (not 1500). Then we can find t from ...

  15000 = 6000(1 +.045/12)^(12t)

  2.5 = 1.00375^(12t) . . . . . divide by 6000

  log(2.5) = 12t·log(1.00375) . . . . . take logarithms

  log(2.5)/(12log(1.00375)) = t ≈ 20.4

It will take 20.4 years for the investment to reach $15,000.