Question

Find the interest earned given the following: Amount needed: $9,350Time in years: 4Interest: 5%Compounded: semiannually

Answer 1

From the question

Invested Amount: $9,350

Time in years: 4

Interest: 5%

Compounded: semiannual

The formula for compound interest is

$A=P(1+\frac{r}{100n})^{nt}$

From the given information

P = $9,350

t = 4

r = 5

Since the amount was compounded semiannually then

n = 2

Substitute these values into the equation

$A=9350(1+\frac{5}{100\times2})^{2\times4}$

Simplify and solve for A

$\begin{gathered} A=9350(1+\frac{5}{200})^8 \\ A=9350(1+0.025)^8 \\ A=9350(1.025)^8 \\ A=11392.07 \end{gathered}$

Interest is given as

$I=A-P$

Hence,

$\begin{gathered} I=11392.07-9350 \\ I=2042.07 \end{gathered}$

Therefore, the interest is $2,042.07