Financial Models

Question

10)  How many years will it take for an initial investment of $10,000 to grow to $35,000? Assume a rate of interest of 2% compounded continuously.

Answer 1

Basically, you you the continuous interest formula A=P * e^rt with the variable:

A: final amount

P: principal or initial amount

r: interest rate (written as a decimal)

t: time (in years)

So, from our problem, we have: A = 35000, P = 10000, and r = 0.02, so we plug those into our formula and solve for t:

35000 = 10000 * e^{0.02 * t}

Divide both sides by 10000:

35000/10000 = e^0.02t

which simplifies to:

7/2 = e^0.02t

Now, take the natual log of both sides:

ln (7/2) = ln(e^0.02t)

Now, we can simplify the right hand side:

ln(7/2) = 0.02t * ln(e)

ln(7/2) = 0.02t * 1

ln(7/2) = 0.02t

Finally: divide both sides by 0.02:

[ln(7/2)]/0.02 = t

t ≈ 62.638 years