Solution:

To solve this problem, we need to use the concept of compounding. When interest is compounded, it means that interest is added to the principal amount, and then interest is calculated on the new amount (principal + interest). The frequency of compounding determines how often interest is added to the principal.

Given:

5% interest payable quarterly

To find:

Interest rate payable annually for a 10-year deposit

Step 1:
Determine the effective annual interest rate when interest is compounded quarterly.

We can use the formula:

Effective annual interest rate = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1

Here, the nominal interest rate is 5%, the number of compounding periods is 4 (since interest is compounded quarterly), and the number of years is 1.

Plugging in the values, we get:

Effective annual interest rate = (1 + (0.05 / 4))^4 - 1
= 1.0509 - 1
= 0.0509 or 5.09%

So, the effective annual interest rate when interest is compounded quarterly is 5.09%.

Step 2:
Determine the interest rate payable annually for a 10-year deposit.

Let the interest rate payable annually be x.

Since the interest is payable annually, the compounding frequency is once a year. So, we can use the formula:

Effective annual interest rate = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1

Plugging in the values, we get:

5.09% = (1 + (x / 1))^1 - 1
5.09% = 1 + x - 1
x = 5.09%

So, the interest rate payable annually for a 10-year deposit is 5.09%.

Conclusion:

Therefore, the interest rate payable annually for a 10-year deposit that is equivalent to 5% interest payable quarterly is 5.09%.

5.09%