What is the interest formula? What if I want to compound monthly or quarterly?

Question

what if the principle is $9400 compounded quarterly for seven months vs. the same amount compounded monthly for seven months. Will the total be the same? What is the formula? Thanks everybody.

Answer 1

See the website below to find your answers.

Answer 2

The formula begins with the annual interest (i) divided by the number of compounding periods (p) in a year; to that result add 1 and then take that result to the power of the number (n) of periods you want the value to compound; finally, multiply that result times your principal value(V).

The formula is V([1+(i/p)]nth

In your example, (assuming 5% annual interest) the monthly compounding of $9400 for 7 months would be calculated:

.05/12 months in a year = .00416

.00416+1= 1.00416

1.00416 to the 7th = 1.0295

1.0295 times 9400 = $9677.30

To see the quarterly result:

.05/4 quarters in a year = .0125

+1 = 1.0125

1.0125 to the 1.75 (since 7 months is 1 and 3/4 quarters)

= 1.0219

1.0219 times 9400 = 9606

This is less money since the interest doesn't begin earning interest as early as with more frequent compounding.

With quarterly compounding, the principal earns money for the first three months.  

With monthly compounding, during the first three months the principal earned inteterst for a month, and then the principal and interest earned interest for a month, and then the principal and interest and the interest on the principal and interest earned interest for a month.