1. Use the compound interest table to find the compound amount earned on a $5,900 deposit for 10 years at 10% compounded semiannually.

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A. 9,610.45
b. 15,654.47
c. 3,710.45
d. 12,375.66

2. Megan deposited $6,000 in an account that pays 4% compounded quarterly. Use the compound interest table to find the interest earned on the investment after 7 years.
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a. 7,680
b. 7,927.74
c. 1,680
d. 1,927.74

I'm confused on these. If you could walk me through it, I'd appreciate it!

interest rate r, compounded n times per year, after t years is

(1+r/n)^(nt)

So, for #1,

5900(1+.10/2)^(2*10) = 15,654.47

#2: 6000(1+.04/4)^(4*7) = 7927.74

Sure! Let's start with the first question.

1. The compound interest formula is given by: A = P(1 + r/n)^(nt), where A is the compound amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have P = $5,900, r = 10% (or 0.10 in decimal form), n = 2 (since it is compounded semiannually), and t = 10 years.

To find the compound amount, we can use the compound interest table. Look for the row with n = 2 and the column with t = 10 years. The corresponding value in the table is 1.61045.

Now, we just need to multiply the principal amount by this value:
A = $5,900 * 1.61045 = $9,610.45

So, the compound amount earned on a $5,900 deposit for 10 years at 10% compounded semiannually is $9,610.45.

Therefore, the correct answer is A. $9,610.45.

Now, let's move on to the second question.

2. Using the same compound interest formula, we can apply it to this question.

We have P = $6,000, r = 4% (or 0.04 in decimal form), n = 4 (since it is compounded quarterly), and t = 7 years.

Again, use the compound interest table to find the corresponding value for n = 4 and t = 7 years. The value in the table is 1.220.

Now, multiply the principal amount by this value:
A = $6,000 * 1.220 = $7,320

The compound amount after 7 years will be $7,320. However, we need to find the interest earned on the investment, which is the difference between the compound amount and the initial principal amount.
Interest = $7,320 - $6,000 = $1,320

Therefore, the interest earned on the investment after 7 years is $1,320.

So, the correct answer is c. $1,320.

I hope this helps! Let me know if you have any further questions.

Sure! I'd be happy to walk you through these questions.

Question 1:
To find the compound amount earned on a deposit using the compound interest table, we need to use the formula:
A = P(1 + r/n)^(nt)

Where:
A = the compound amount (the final amount after earning interest)
P = the principal amount (the initial deposit)
r = the interest rate per period
n = the number of compounding periods per year
t = the number of years

In this case, P = $5,900, r = 10% (or 0.10), n = 2 (since it is compounded semiannually), and t = 10 years.

Step 1: Convert the interest rate to decimal form
r = 10% = 0.10

Step 2: Plug in the values into the formula
A = 5900(1 + 0.10/2)^(2*10)

Step 3: Simplify the equation
A = 5900(1 + 0.05)^20

Step 4: Use the compound interest table to find the compound amount for the given interest rate and number of years. In this case, the compound amount is closest to $9,610.45 (option A).

Question 2:
Similarly, to find the interest earned on an investment using the compound interest table, we can use the formula mentioned earlier.

In this case, P = $6,000, r = 4% (or 0.04), n = 4 (since it is compounded quarterly), and t = 7 years.

Step 1: Convert the interest rate to decimal form
r = 4% = 0.04

Step 2: Plug in the values into the formula
A = 6000(1 + 0.04/4)^(4*7)

Step 3: Simplify the equation
A = 6000(1 + 0.01)^28

Step 4: Use the compound interest table to find the compound amount for the given interest rate and number of years. In this case, the compound amount is closest to $7,927.74 (option B).

So, the answers to the questions are:
1. The compound amount earned on a $5,900 deposit for 10 years at 10% compounded semiannually is approximately $9,610.45 (option A).
2. The interest earned on a $6,000 investment for 7 years at 4% compounded quarterly is approximately $7,927.74 (option B).