Question

Steven invests $20,000 in an account earning 3% interest, compounded annually for 10 years. Three years after Stevens's initial investment, Evan invests $10,000 in an account earning 7% interest, compounded annually for 7 years. Given that no additional deposits are made, compare the amount of interest earned after the interest period ends for each account. (round to the nearest dollar)

Answer 1

The answer is B)Steven earned $820 more in interest in his account than Evan.

Answer 2

Firstly , let's calculate for STEVEN

Principal = $20,000

Rate = 3%= 0.03 ( compounded annually)

Time = 10 years

Now the formula for Amount after 10 years will be

$A=P(1+\frac{r}{n})^{(nt)}$

where , A is amount after t years , P is the principal i.e. Initial Investment, r= rate of interest , n = number of compounding intervals , t = number of years

n=1 , because compounded annually

So

$A=20,000(1+\frac{0.03}{1})^{((1)(10))}$

$A=20,000(1.03)^{10}$

We can now plug in the calculator for the answer

So A=$26878.33

It means Interest in this case will be

Interest = Amount - Principal = $26,878.33 - $20,000

Interest = $6878.33

Now let's calculate for EVAN

Principal = $10,000

Rate = 7% = 0.07 ( compounded annually , n=1)

Time = 7 years

$A=P(1+\frac{r}{n})^{(nt)}$

Let's plug the values

$A=10,000(1+\frac{0.07}{1})^{((1)(10))}$

$A=10,000(1.07)^{10}$

Plug in the calculator

A= $19671.51

Interest = Amount- principal = $19671.51 - $10000

Interest = $9671.51

Now we have to compare the Interest earned by both of them

$9671.51 - $6878.33 = $2793.18

So , Evan earned $2793.18 more interest than Steven