Question

Suppose that $15,000 is deposited for five years at 3% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.

Answer 1

The interest earned on a $15,000 deposit at 3% APR compounded semiannually for five years is $2405.43 when rounded to the nearest cent.

Step-by-step explanation:

To calculate the interest earned on a $15,000 deposit at 3% APR compounded semiannually for five years, we use the formula for compound interest:

A = P (1 + r/n)^(n*t)

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

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

t is the time the money is invested for in years.

For this example:

• P = $15,000
• r = 3% or 0.03 (as a decimal)
• n = 2 (since the interest is compounded semiannually)
• t = 5

Now, let's plug these values into the formula:

• A = 15000 * (1 + 0.03/2)^(2*5)
• A = 15000 * (1 + 0.015)^10
• A = 15000 * (1.015)^10
• A = 15000 * 1.16036233
• A = 17405.43

To find the interest earned, we subtract the principal from the total amount:

Interest earned = A - P

Interest earned = 17405.43 - 15000

Interest earned = $2405.43

The interest earned on a $15,000 deposit at 3% APR compounded semiannually for five years is $2405.43, rounded to the nearest cent.

Answer 2

Step 1

State the formula for compound interest

`A=P(1+(r)/(n))^(nt)`

where;

`\begin{gathered} P=15000 \\ r=(3)/(100)=0.03 \\ n=2 \\ t=5 \end{gathered}`

Step 2

Find the interest earned if the interest is compounded semiannually.

`\begin{gathered} A=15000(1+(0.03)/(2))^(2*5) \\ A=15000(1.015)^(10) \\ A=15000(1.160540825) \\ A=\text{ \$}17408.11238\text{ } \end{gathered}`

The Amount(A)=Interest(I) +Principal(P)

Therefore;

`\begin{gathered} 17408.11238=I\text{ +15000} \\ I=\text{ \$}2408.112375 \\ I=\text{ \$2408.11} \end{gathered}`

Answer; Interest=$2408.11