Questions: Justin borrowed 9700 at 3 1/2% for 6 years compounded quarterly. What is the compound amount (Future Value) of the loan and how much interest will he pay on the loan? Use a TVM Solver to answer the question. State the values used for calculations. Type "0" (Zero) if that variable was not used. Round all decimals to 3 decimal places for the table. n= i%= PV= PMT= FV= Answer the questions. Round final answers to the nearest cent. All answers should be positive. Compound amount = Compound interest =

Justin borrowed 9700 at 3 1/2% for 6 years compounded quarterly. What is the compound amount (Future Value) of the loan and how much interest will he pay on the loan? Use a TVM Solver to answer the question. State the values used for calculations. Type "0" (Zero) if that variable was not used. Round all decimals to 3 decimal places for the table. n= i%= PV= PMT= FV= Answer the questions. Round final answers to the nearest cent. All answers should be positive. Compound amount = Compound interest =
Transcript text: Justin borrowed $\$ 9700$ at $3 \frac{1}{2} \%$ for 6 years compounded quarterly. What is the compound amount (Future Value) of the loan and how much interest will he pay on the loan? Use a TVM Solver to answer the question. State the values used for calculations. Type "0" (Zero) if that variable was not used. Round all decimals to 3 decimal places for the table. \[ \begin{array}{ll} \mathrm{n}= & \square \\ \mathrm{i} \%= & \square \\ \mathrm{PV}= & \square \\ \mathrm{PMT}= & \square \\ \mathrm{FV}= & \square \end{array} \] Answer the questions. Round final answers to the nearest cent. All answers should be positive. Compound amount $=\$$ $\square$ Compound interest $=\$$ $\square$
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Solution

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Solution Steps

To solve this problem, we need to use the formula for compound interest to find the future value (FV) of the loan and then calculate the compound interest. The formula for compound interest is:

\[ FV = PV \left(1 + \frac{r}{n}\right)^{nt} \]

Where:

  • \( PV \) is the present value (initial amount) which is $9700.
  • \( r \) is the annual interest rate (as a decimal), which is \( 3.5\% = 0.035 \).
  • \( n \) is the number of times the interest is compounded per year, which is 4 (quarterly).
  • \( t \) is the number of years, which is 6.

Once we have the future value, the compound interest can be found by subtracting the present value from the future value.

Step 1: Given Values

We start with the following values:

  • Present Value (\( PV \)): \( 9700 \)
  • Annual Interest Rate (\( r \)): \( 3.5\% = 0.035 \)
  • Compounding Frequency (\( n \)): \( 4 \) (quarterly)
  • Time Period (\( t \)): \( 6 \) years
Step 2: Calculate Future Value

Using the formula for compound interest:

\[ FV = PV \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the values:

\[ FV = 9700 \left(1 + \frac{0.035}{4}\right)^{4 \times 6} \]

Calculating this gives:

\[ FV = 9700 \left(1 + 0.00875\right)^{24} = 9700 \left(1.00875\right)^{24} \approx 11955.75 \]

Step 3: Calculate Compound Interest

The compound interest can be calculated as:

\[ \text{Compound Interest} = FV - PV \]

Substituting the values:

\[ \text{Compound Interest} = 11955.75 - 9700 = 2255.75 \]

Final Answer

The compound amount is \( \boxed{11955.75} \) and the compound interest is \( \boxed{2255.75} \).

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