You are looking at opening a savings account and have seen that ANZ Bank seems to be offering a good rate on one of their accounts. The account would pay interest monthly. You work out that if you put $1000 in this account, you would have $1012.07 in your account at the end of the year. What would the advertised rate on this account be?a.None of them.b.0.1% per monthc.1% p.a. compounding monthlyd.1.2004% p.a. compounding monthlye.1.207% p.a.
Question
You are looking at opening a savings account and have seen that ANZ Bank seems to be offering a good rate on one of their accounts. The account would pay interest monthly. You work out that if you put 1012.07 in your account at the end of the year. What would the advertised rate on this account be?a.None of them.b.0.1% per monthc.1% p.a. compounding monthlyd.1.2004% p.a. compounding monthlye.1.207% p.a.
Solution
The correct answer is d. 1.2004% p.a. compounding monthly.
Here's how you can calculate it:
First, you need to find out the monthly growth rate. Since you start with 1012.07 at the end of the year, the total growth over the year is 1000 = 1.01207.
Since interest is compounded monthly, you need to take the 12th root of this total growth to find the monthly growth rate: (1.01207)^(1/12) = 1.000993.
To convert this monthly growth rate into an annual interest rate, you subtract 1 and multiply by 12: (1.000993 - 1) * 12 = 0.012004 or 1.2004%.
So, the advertised rate would be 1.2004% p.a. compounding monthly.
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