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# how in calculate interest in months vs years

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How do you calculate intrest in months vs years?

Guest Apr 5, 2015

#1
+92256
+5

This is a very good question and really confuses a lot of students.

The compound interest formula is

$$FV=P(1+r)^n$$

FV stands for future value and P stands for principal - that is how much you start with.

When you are introduced to this in year nine you are told that r is your interest rate and n is the time.

This is true BUT  the interest rate is stated as an annual interest rate and the time is stated in years so kids often get it cemented into their brains that  r is the (annual) rate and n is the time (years).  This is WRONG!

r is the interest rate for the compounding period of time.

and

n is the number of compounding time periods.

SO     if the interest is 6% per annum compounding quarterly and the money is invested for 2 years then

the interest is compunded 4 times every year so each time it must be a quarter of 6%

$$r=\frac{6\%}{4}=\frac{0.06}{4}=0.015$$

and

the interest is compounded 4 times a year for 2 years so that is

$$n=4*2 = 8$$     compounding periods

sorry I just read your question better. If it were compounding monthly then r=6%/12  and n=2*12

----------------------------------------------------------------------------------

Sometimes different letters are used - but this is always the idea behind it.

sometimes the formual is written like this

$$PV=P(1+\frac{r}{t})^{n*t}$$

Where r is the annual rate, n is the number of years and t is the number of compounding periods each year.

but it really is the same.   (although n and r stand for the yearly figures not the compounding period figures)

Melody  Apr 6, 2015
Sort:

#1
+92256
+5

This is a very good question and really confuses a lot of students.

The compound interest formula is

$$FV=P(1+r)^n$$

FV stands for future value and P stands for principal - that is how much you start with.

When you are introduced to this in year nine you are told that r is your interest rate and n is the time.

This is true BUT  the interest rate is stated as an annual interest rate and the time is stated in years so kids often get it cemented into their brains that  r is the (annual) rate and n is the time (years).  This is WRONG!

r is the interest rate for the compounding period of time.

and

n is the number of compounding time periods.

SO     if the interest is 6% per annum compounding quarterly and the money is invested for 2 years then

the interest is compunded 4 times every year so each time it must be a quarter of 6%

$$r=\frac{6\%}{4}=\frac{0.06}{4}=0.015$$

and

the interest is compounded 4 times a year for 2 years so that is

$$n=4*2 = 8$$     compounding periods

sorry I just read your question better. If it were compounding monthly then r=6%/12  and n=2*12

----------------------------------------------------------------------------------

Sometimes different letters are used - but this is always the idea behind it.

sometimes the formual is written like this

$$PV=P(1+\frac{r}{t})^{n*t}$$

Where r is the annual rate, n is the number of years and t is the number of compounding periods each year.

but it really is the same.   (although n and r stand for the yearly figures not the compounding period figures)

Melody  Apr 6, 2015

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