Question

How much interest did she earn? (compound interest)

Anne inherited some money from her grandfather and put it in a bank account that earns 10% interest compounded quarterly. After 4 years, Anne had $600.00 in the bank account. How much interest did she earn? (ROUND TO THE NEAREST CENT)

Answer 1

Total Interest of 4 years is: `$195.83`

Explanation:

Given:
Annual compound interest is 10%
Calculation cycle: 4 times a year.
Final sum in account: $600.00 after 4 years.

Let the initial unknown principle sum be `P`
Let the total interest in dollars be `x`
Let the count of years be `n=4`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`P(1+10/(nxx100))^(4n) =" total in the account"=$600`

As the is a cycle of 4 calculations per year we have the indices of `4n`

This is over 4 years so `n=4` giving:

`P(1+10/(400))^(16) =$600`

`P(410/(400))^(16) =$600`

`P=$600-:(410/400)^(16) = $404.17496...`

Rounding gives: `P=$404.17`

Thus the interest is the difference.

`$600.00`
`ul($404.17 larr" Subtract")`
`$195.83`

Answer 2

`color(blue)($195.83)`

Explanation:

Compound interest is given by the formula:

`"FV"="PV"(1+r/n)^(nt)`

Where:

`FV=" future value"`

`PV = " present value"`

`bbr=" interest rate"` ( Given as a decimal )

`bbn= " compounding period"`

`bbt= " time in years"`

We are give interest rate of `10%` so.

`r=10/100=0.1`

compounding period is quarterly so,

`n=4`

Time period is 4 years so:

`t=4`

`FV =600`

To find the amount of interest earned, we first need to find the present value:

Using:

`"FV"="PV"(1+r/n)^(nt)`

`600=PV(1+0.1/4)^16`

`600=PV(1.025)^16`

`PV=600/((1.025)^16)=404.1749600`

Interest earned is:

`FV-PV`

`600-404.1749600=195.8250400`

`$195.83` to nearest cent.