ANSWER

Calculating the Advertised Interest Rate for ANZ Bank’s Monthly Compounding Savings Account”

To determine the advertised interest rate on the savings account offered by ANZ Bank, we can use the formula for compound interest:

�=�(1+��)��A=P(1+nr​)nt

Where:

$A$ is the future amount of money in the account.

$P$ is the initial principal amount ($1000 in this case).

$r$ is the annual interest rate (the rate we want to find).

$n$ is the number of times the interest is compounded per year (monthly, in this case).

$t$ is the number of years (1 year in this case).

We are given that after 1 year, the account balance will be $1012.07.

Plugging in the values:

1012.07=1000(1+�12)12⋅11012.07=1000(1+12r​)12⋅1

Now, we need to solve for $r$.

Let’s simplify the equation step by step:

Divide both sides by 1000:

1012.071000=(1+�12)1210001012.07​=(1+12r​)12

Now, take the 12th root of both sides:

(1012.071000)112=1+�12(10001012.07​)121​=1+12r​

Subtract 1 from both sides:

(1012.071000)112−1=�12(10001012.07​)121​−1=12r​

Now, multiply both sides by 12 to isolate $r$:

�=12((1012.071000)112−1)r=12((10001012.07​)121​−1)

Now, calculate the value within the parentheses:

(1012.071000)112−1≈0.012004(10001012.07​)121​−1≈0.012004

Now, multiply by 12:

$r\approx 12\cdot 0.012004\approx 0.14405$

So, the annual interest rate ($r$) is approximately 0.14405 or 14.405%.

Now, let’s check the options provided:

a. 1% p.a. compounding monthly – This is too low. b. 1.2004% p.a. compounding monthly – This matches our calculated rate (approximately 1.2004%). c. 1.207% p.a. – Close but not exactly the same as our calculated rate. d. 0.1% per month – This is much higher than our calculated rate. e. None of them – This is not correct since option (b) matches our calculated rate.

So, the correct answer is option (b): 1.2004% p.a. compounding monthly.