# Find the amount of money in an account after 5 years if \$2800 is deposited at 7% annual interest compounded monthly.

Quick answer:

The amount of money in the account after 5 years is \$3969.35 for the given compounding parameters.

## Expert Answers

Hello!

When money is deposited, an annual rate is usually stated and fixed. Most often, this annual rate is formulated in percent form, `r = x % . ` If the money is compounded once a year (yearly), the rate is used directly: a present value `P ` gets increased by `P * x % = P * x / 100 . ` Then the future value after one year is equal to `F_1 = P ( 1 + x / 100 ) . ` After n years it becomes `F_n = P ( 1 + x / 100 )^n , ` which is a geometric progression.

But in some setups compounding appears more frequently. In our task it appears once a month which means `12 ` times a year. In such a case the annual rate is divided by `12 ` and used each month: `P ( 1 + ( x / 12 ) / 100 ) ` after one month,

`F_1 = P ( 1 + ( x / 12 ) / 100 )^12` after one year.

After `m ` years, the future value gets multiplied `m ` times by `( 1 + ( x / 12 ) / 100 )^12 , ` so the formula is

`F_m = P ( 1 + ( x / 12 ) / 100 )^( 12 * m ) .`

Substitute the given values `P = \$ 2800 , ` `x = 7 , ` `m = 5 ` and obtain

`F_5 = \$ 2800 * ( 1 + 7 / 1200 )^60 approx ` \$3969.35.

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