Question

You deposit $2000 into an account that earns interest at the rate of 5% per year. How much interest is obtained over 5 years?

Answer 1

$500

Explanation:

We know Simple Interest (`SI`)= `PxxR/100xxT`

Where P = Principal amount, R = Rate of interest and. T = Time.

Here P = 2000, I = 5 and T = 5.

Hence `SI = 2000xx5/100xx5 = 500`

Answer 2

`color(brown)("The question does not declare the interest type used")`

`$566.72` to 2 decimal places `larr` compound interest

`$500.00` to 2 decimal places `larr` simple interest

Explanation:

`color(blue)("Compound interest")`

`color(brown)("In real life this is the one that would be used")`

The annual interest is distributed over each payment cycle.

For monthly calculation cycle we do have `color(white)("ddd")1/12xx5/100 = 5/1200`

Using `P(1+5/1200)^t`

Note that `t` is for 5 years at 12 cycles per year giving:

`$2000(1+5/1200)^60`

`$2000(1205/1200)^60 = $2566.72` to 2 decimal places

Interest is

`$2566.72`
`ul($2000.00 larr" Subtract")`
`color(white)("d")$566.72`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Simple interst")`

`5% ->5/100`

Interest per year `5/100 xx$2000 = $100`

Interest for 5 years `color(white)("d") 5xx $100 = $500`