Assume the initial investment was $6600 and the annual interest

rate to be compounded continuously is 5%. Assume also that
the target amount is $7900.

If you want the account to contain the target amount given above after
9 years, what yearly interest rate is needed?

Pt = Po * e^rt,

7900 = 6600 * e^9r,
Divide both sides by 6600:
e^9r = 7900/6600 = 1.1970,
9r = ln(1.1970) = 0.1798,
r = 0.1798/9 = 0.02 = 2%.

To find the yearly interest rate needed to achieve the target amount after 9 years, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A is the final amount (target amount)
P is the principal (initial investment)
e is the base of the natural logarithm (approximately 2.71828)
r is the continuous interest rate
t is the time in years

In this case, the initial investment (P) is $6600, the target amount (A) is $7900, the time (t) is 9 years, and we need to find the continuous interest rate (r).

First, we can rearrange the formula to solve for the continuous interest rate (r):

r = ln(A/P) / t

Now, we can plug in the values:

r = ln(7900/6600) / 9

Calculating this using natural logarithm:

r ≈ ln(1.1969697) / 9
r ≈ 0.17919 / 9
r ≈ 0.01991

So, the yearly interest rate needed to achieve the target amount of $7900 after 9 years is approximately 1.991%.