2. Angie deposited $\$ 10,000$ into a savings account that offered an interest rate of $4.5 \% \mathrm{c} / \mathrm{d}$. She left the deposit for 5 years, then took the balance and put it into another account that would pay her $\$ 500 /$ month, with the first payment being made on the day of deposit. This account earns interest of $3.9 \% \mathrm{c} / \mathrm{m}$. How many payments will Angie receive? (round your answer to the next higher integer) (2 marks)

Step 1 ：First, we calculate the total amount in the savings account after 5 years with an interest rate of 4.5%. The formula for compound interest is \(A = P(1 + r/n)^{nt}\), where \(P = \$10,000\), \(r = 4.5\% = 0.045\), \(n = 1\) (compounded annually), and \(t = 5\) years. Substituting these values into the formula, we get \(A = \$10,000(1 + 0.045/1)^{1*5} = \$12,461.82\).

Step 2 ：Next, we calculate how many months it will take for the total amount to be depleted at a rate of \$500 per month with an interest rate of 3.9%. The formula for the number of payments for an ordinary annuity is \(n = \frac{\log(1 - \frac{rP}{A})}{\log(1 + r)}\), where \(P = \$500\), \(r = 3.9\% = 0.039/12 = 0.00325\) (monthly interest rate), and \(A = \$12,461.82\). Substituting these values into the formula, we get \(n = \frac{\log(1 - \frac{0.00325*\$500}{\$12,461.82})}{\log(1 + 0.00325)} = 26.4\).

Step 3 ：Since the number of payments cannot be a fraction, we round up to the next higher integer, which is 27.

Step 4 ：Final Answer: Angie will receive \(\boxed{27}\) payments.