Question

The formula is A=P(1+r/n)^nt8. Oswald Chesterfield Cobblepot invests $5,000 into an account that earns 2.5% interestcompounded monthly.a. How much money is in the account after two years? Use the formula above.Answer:b. How much money in interest was earned?Answer:

Answer 1

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:

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

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

$P=5000,r=\frac{2.5}{100}=0.025,t=2,n=12\text{ since it is compounded monthly}$

STEP 3: Calculate the Compounded Amount

$\begin{gathered} A=5000(1+\frac{0.025}{12})^{2\times12} \\ A=5000(1+0.002083333333)^^{24} \\ A=5000\times1.0020833333^{24} \\ A=5000\times1.05121642 \\ A=5256.0821 \\ A\approx5256.08 \end{gathered}$

STEP 4: Calculate the compounded interest

$\begin{gathered} Interest=Amount-Principal \\ \text{By substitution,} \\ Interest=5256.08-5000 \\ Interest=256.08 \end{gathered}$

Hence,

$5256.08 was in the account after 2 years

The interest earned was $256.08