Question

If $12000 is invested at 4% compound quarterly, what is the amount after 8 years?

Answer 1

`$16,499.29`

Explanation:

okay so we are interested in years and we know there are 4 quarters in a year so quarterly compounded interest is
`.04/4 = .01`

now for the first quarter it would be
`y_1=12000*(1.01)`

quarter two is whatever was made in quarter 1 plus quarter 2
`y_2=y_1*(1.01)` or `12000*(1.01)*(1.01)`

this relates to the following for years
`f(n) = 12000*(1.01)^(4*n)`
`f(8) = 12000*(1.01)^32 = 16499.2881424`

Answer 2

`color(lime)($16,499.29)`

Explanation:

Use the interest formula: `A = P(1+r/n)^(nt)`

Where:

`color(darkblue)(P` = initial investment
`color(darkgreen)(r` = annual interest rate
`color(crimson)(n` = amount of times interest is compounded (one year)
`color(magenta)(t` = years (amount)

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Now we can gather our knowledge and use the formula to find what we need to know. Start by plugging in values already known. Remember to convert the percent rate into a decimal.

`A = color(darkblue)(12000)(1+color(darkgreen)(0.04)/color(crimson)(4))^((color(crimson)(4)*color(magenta)(8)))`

Find `A` by simplifying the right side.

`color(lime)(A) = 12000(1+0.01)^(32)`

`color(lime)(A) = 12000(1.01)^(32)`

`color(lime)(A) = 12000(1.37494067853)`

`color(lime)(A) = 16499.2881424`

Please note, a calculator was used to keep computation accurate. Always use a calculator and round the final answer, never round a number during the process if at all possible.

`A~~color(lime)16499.29`

So, 8 years after investing, you get about `color(lime)($16,499.29`.