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

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Answer 1 · 2017-12-17T12:42:24

$500

We know Simple Interest ( $S I$ $SI$ )= $P \times \frac{R}{100} \times T$ $PxxR/100xxT$

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

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

Hence $S I = 2000 \times \frac{5}{100} \times 5 = 500$ $SI = 2000xx5/100xx5 = 500$

Answer 2 · 2017-12-17T13:06:24

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

$$ 566.72$ $$566.72$ to 2 decimal places $\leftarrow$ $larr$ compound interest

$$ 500.00$ $$500.00$ to 2 decimal places $\leftarrow$ $larr$ simple interest

$Compound interest$ $color(blue)("Compound interest")$

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

The annual interest is distributed over each payment cycle.

For monthly calculation cycle we do have $ddd \frac{1}{12} \times \frac{5}{100} = \frac{5}{1200}$ $color(white)("ddd")1/12xx5/100 = 5/1200$

Using $P {(1 + \frac{5}{1200})}^{t}$ $P(1+5/1200)^t$

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

$$ 2000 {(1 + \frac{5}{1200})}^{60}$ $$2000(1+5/1200)^60$

$$ 2000 {(\frac{1205}{1200})}^{60} = $ 2566.72$ $$2000(1205/1200)^60 = $2566.72$ to 2 decimal places

Interest is

$$ 2566.72$ $$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 = $500$