To solve the problem, we use the formula for compound interest:

$A = P \times (1 + r)^t$

Where:

• $A$ is the final amount (£14,569.93),
• $P$ is the principal (the initial investment, which we are solving for),
• $r$ is the annual interest rate (9% = 0.09),
• $t$ is the time in years (15 years).

Rearranging the formula to solve for $P$:

$P = \frac{A}{(1 + r)^t}$

Substituting the given values: $P = \frac{14,569.93}{(1 + 0.09)^{15}}$

Let me calculate this for you. Given values A = 14569.93 # Final amount in pounds r = 0.09 # Annual interest rate t = 15 # Time in years

Calculate the initial investment (P)

P = A / ((1 + r) ** t) round(P) # Rounded to the nearest £1The initial investment Abigail made was £4,000, rounded to the nearest pound.

Would you like a detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:

1. What would the final amount be if the interest rate were 8% instead of 9%?
2. How does the formula change for simple interest instead of compound interest?
3. What is the effect of doubling the investment period (e.g., 30 years instead of 15)?
4. How much would need to be invested initially to achieve £20,000 in 15 years at 9% interest?
5. What would be the effective interest rate if compounded quarterly instead of annually?

Tip: Always double-check the compounding frequency (e.g., yearly, quarterly) to ensure accurate calculations!