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Sagot :
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given formula with definition of terms
Compounded Amount is gotten using:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]Where:
A =final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
STEP 2: Write the given parameters
[tex]P=5000,r=\frac{2.5}{100}=0.025,t=2,n=12\text{ since it is compounded monthly}[/tex]STEP 3: Calculate the Compounded Amount
[tex]\begin{gathered} A=5000(1+\frac{0.025}{12})^{2\times12} \\ A=5000(1+0.002083333333)^^{24} \\ A=5000\times1.0020833333^{24} \\ A=5000\times1.05121642 \\ A=5256.0821 \\ A\approx5256.08 \end{gathered}[/tex]STEP 4: Calculate the compounded interest
[tex]\begin{gathered} Interest=Amount-Principal \\ \text{By substitution,} \\ Interest=5256.08-5000 \\ Interest=256.08 \end{gathered}[/tex]Hence,
$5256.08 was in the account after 2 years
The interest earned was $256.08
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