Question

What is the value of $600 per quarter for four years at the rate of 8% compounded quarterly?

Answer 1

`T_(c=16)=$823.67` to 2 decimal places

Explanation:

`color(purple)("Assumption: The 8% is the annual rate.")`

There are 4 of these calculations per years so instead of using 8% at each calculation we use `(8%)/4` per calculation 4 times a years. Which is `=8/400`

Let `n` be the number of years
Let the count of calculations be `c=4n`

Let the principle sum be `P`
Let the Total in the account at count c be `T_c`

Then we have:

`T_c=P(1+8/400)^(4n)`
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You ask: `color(purple)("what is the value of $600 per quarter for 4 years")`

This implies an output of a list comprising of the progressive value of the $600 plus interest at each quarterly stage over the 4 years.

`color(purple)("Another assumption")`
Calculating for the total of compounded interest plus the principle sum `ul("after completion of 4 years.")`

`T_c=$600(1+8/400)^(16) = $823.6714....`

`T_(c=16)=$823.67` to 2 decimal places

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