Tina inherits $60,000 and invests it in an account earning interest at a rate of 0.5% per month - HSC - SSCE Mathematics Advanced - Question 26 - 2020 - Paper 1

To calculate the total interest earned in the first three months:

1. Total withdrawals after 3 months: $800 imes 3 = 2400$

2. Initial balance was $60,000, and the balance after three withdrawals is: $60,000 - 58,492.49 = 1,507.51$

3. Thus, the interest earned is: $2400 - 1,507.51 = 892.49$

So, the interest earned in the first three months is $892.49.

To find the amount in the account after 94 withdrawals, we can derive a formula:

1. The recurrence relation can be expressed as:
   A_n = 60,000(1.005)^n - 800 imes rac{(1.005^n - 1)}{0.005}
   This formula accounts for the interest accumulated and the total withdrawals.

2. For $n = 94$:
   A_{94} = 60,000(1.005)^{94} - 800 imes rac{(1.005^{94} - 1)}{0.005}
   Calculating this yields approximately:
   $A_{94} ext{ is about } 187.85$.

Thus, the amount of money in the account immediately after the 94th withdrawal is approximately $187.85.