Question

Find the missing interest earned. (round to the nearest cent as needed)

Answer 1

The compound interest is $625.41

Here, we want to calculate the missing amount, which is the interest earned

Mathematically, this is the difference between the amount that the compounding will yield and the principal

We can calculate the amount earned using the formula below;

`A\text{ = P(1 + }(r)/(n))^(nt)`

where;

P is the principal = $1,000

r is the interest rate = 7% which is same as 7/100 = 0.07

n is the number of times the interest is compounded per year

According to the question, the compounding is quarterly which means 4 times per year

so n = 4

t represents the number of years = 7

Substituting these values into the equation, we have;

`\begin{gathered} A\text{ = 1000(1 + }(0.07)/(4))^(7*4) \\ \\ A=1000(1+0.0175)^(28) \\ \\ A=1000(1.0175)^(28) \\ \\ A\text{ = 1,625.41} \end{gathered}`

So now, we can get the compound interest using the formula below;

`\begin{gathered} \text{compound interest = Amount - Principal} \\ \\ =\text{ 1,625.41-1000 = 625.41} \end{gathered}`