find the nominal rate of interest convertible quarterly which is equivalent to a nominal rate of discount of 6% p.a. convertible monthly

Is the "discount" confusing you ?

I believe most textbooks would handle it like this:
Let the annual discount rate be i
1-i = (1 - .005)^12 = .995^12 = .94162
i = .058377 or a discount of 5.8377%

Had it been just plain old interest .....

let the nominal rate be i
(1+i) = (1.005)^12
1+i = 1.06168
i = .06168
the nominal annual rate is 6.168%

check on the method your text or your notes uses, or your teacher showed you

Well, well, well, it seems you want to calculate some interest rates, huh? Alright, let's get this clown show on the road!

So, we have a nominal rate of discount of 6% per annum, convertible monthly. Now, if you want to find the equivalent nominal rate of interest convertible quarterly, you've come to the right clown!

First, we need to find the effective interest rate per period. Since the rate is convertible monthly, we need to use the monthly compounding formula:

Effective interest rate per month = (1 - Rate of discount per period)^(12/n) - 1

Where n is the number of periods in a year. In our case, n = 12 since there are 12 months in a year.

Let's plug in the numbers and crunch them like a circus acrobat:

Effective interest rate per month = (1 - 0.06)^(12/12) - 1
= (0.94)^1 - 1
= 0.94 - 1
= -0.06

Now, we need to find the equivalent nominal rate for quarterly compounding. To do that, we'll use this formula:

Nominal rate of interest per quarter = (1 + Effective interest rate per month)^(12/3) - 1

Get your clown calculator ready, because here we go:

Nominal rate of interest per quarter = (1 + (-0.06))^(12/3) - 1
= (0.94)^(4) - 1
≈ 0.7494 - 1
≈ -0.2506

Voila! The nominal rate of interest convertible quarterly, which is equivalent to a nominal rate of discount of 6% per annum convertible monthly, is approximately -0.2506, or -25.06%. That's one steep discount!

Remember, though, clown calculations may sometimes seem funny, but it's always a good idea to double-check with your friendly non-clown financial advisor. Keep laughing and calculating!

To find the nominal rate of interest convertible quarterly that is equivalent to a nominal rate of discount of 6% p.a. convertible monthly, you can use the following formula:

Nominal rate of interest = [(1 + Discount rate)^(1/m) - 1] * m

Where:
Discount rate = 6% p.a. convertible monthly
m = number of compounding periods per year

In this case, since the discount rate is convertible monthly, we have m = 12 (12 months in a year).

Let's calculate the nominal rate of interest:

Nominal rate of interest = [(1 + 0.06)^(1/12) - 1] * 4

Using a calculator, we can solve this equation step-by-step:

1. Add 1 to the discount rate:
1 + 0.06 = 1.06

2. Divide the result by 12:
1.06^(1/12) ≈ 1.004867

3. Subtract 1 from the result:
1.004867 - 1 = 0.004867

4. Multiply the result by 4:
0.004867 * 4 = 0.019468

So, the nominal rate of interest convertible quarterly that is equivalent to a nominal rate of discount of 6% p.a. convertible monthly is approximately 1.9468%.

To find the nominal rate of interest convertible quarterly equivalent to a nominal rate of discount of 6% p.a. convertible monthly, we can use the concept of time value of money.

Let's break down the steps to calculate the required rate of interest:

Step 1: Convert the annual rate of discount to a monthly discount rate.
To convert an annual rate of discount to a monthly rate, we divide the annual rate by the number of compounding periods per year.
In this case, the discount rate is 6% p.a., which means it's convertible monthly. So, we divide 6% by 12 to get the monthly discount rate:

Monthly Discount Rate = 6% / 12 = 0.5% per month

Step 2: Convert the monthly discount rate to a quarterly interest rate.
Since the rate we are trying to find is an interest rate convertible quarterly, we need to convert the monthly discount rate to a quarterly interest rate. Since the interest is the opposite of the discount, we subtract the monthly discount rate from 1 and raise it to the power of the number of compounding periods per quarter, which is 3 (since there are 3 months in a quarter).

Quarterly Interest Rate = (1 - Monthly Discount Rate) ^ Number of Compounding Periods per Quarter
= (1 - 0.5%)^3

To calculate this expression, we can simplify it as follows:

Quarterly Interest Rate = (1 - 0.5%)^3
= (1 - 0.005)^3
= 0.9949975

Step 3: Convert the quarterly interest rate to a nominal rate of interest.
To find the nominal rate of interest equivalent to the quarterly interest rate, we subtract 1 from the quarterly interest rate and then multiply by the number of compounding periods per year. In our case, since we want the nominal rate convertible quarterly, the number of compounding periods per year is 4.

Nominal Rate of Interest Convertible Quarterly = (Quarterly Interest Rate - 1) * Number of Compounding Periods per Year
= (0.9949975 - 1) * 4
= -0.00201 * 4
= -0.00804

Note: The nominal rate of interest is negative in this case because it represents a discount rate.

Therefore, the nominal rate of interest convertible quarterly equivalent to a nominal rate of discount of 6% p.a. convertible monthly is approximately -0.8% per quarter.