Questions: Question 14
Savings and the TVM Calculator
Use the TVM Calculator to solve the following savings problem. Round your result to two decimal places as needed.
Ray makes an investment of 9,500 into an account that pays interest compounded annually. In addition, he makes a yearly deposit of 120. At the end of 4 years, his balance is 14,500.
What interest rate was earned on his investment?
Enter the values you need to put in the TVM calculator. Remember that money paid to the bank is negative and money received from the bank is positive.
NOTE: Put the letter x in the answer box for the unknown value in the appropriate box below. The number solution will go in the final box in the last question.
PV=, N=, Present Value
Number of Compounding Periods
Payment =, 1 %=, Annual Interest Rate as a Percent
FV=, P/Y and C/Y=, Payments per Year and/or Compoundings per Year
Ray earned an interest rate of % on his investment.
Transcript text: Question 14
Savings and the TVM Calculator
Use the TVM Calculator to solve the following savings problem. Round your result to two decimal places as needed.
Ray makes an investment of $\$ 9,500$ into an account that pays interest compounded annually. In addition, he makes a yearly deposit of $\$ 120$. At the end of 4 years, his balance is $\$ 14,500$.
What interest rate was earned on his investment?
Enter the values you need to put in the TVM calculator. Remember that money paid to the bank is negative and money received from the bank is positive.
NOTE: Put the letter $x$ in the answerbox for the unknown value in the appropriate box below. The number solution will go in the final box in the last question.
\begin{tabular}{|l|l|}
\hline $\mathrm{PV}=\square$ & \begin{tabular}{l}
$\mathrm{N}=\square$ \\
Present Value
\end{tabular} \\
\hline Number of Compounding Periods \\
Payment $=\square$ & \begin{tabular}{l}
$1 \%=\square$ \\
Annual Interest Rate as a Percent
\end{tabular} \\
\hline $\mathrm{FV}=\square$ & \begin{tabular}{l}
P/Y and $\mathrm{C} / \mathrm{Y}=\square$ \\
Payments per Year and/or \\
Compoundings per Year
\end{tabular} \\
\hline
\end{tabular}
Ray earned an interest rate of $\square$ \% on his investment.
Solution
Solution Steps
Step 1: Identify Given Values
We have the following values for Ray's investment:
Present Value (\(PV\)) = \(-9500\)
Annual Payment (\(PMT\)) = \(-120\)
Future Value (\(FV\)) = \(14500\)
Number of Years (\(N\)) = \(4\)
Step 2: Set Up the Future Value Equation
The future value of an investment with annual deposits can be expressed as:
\[
FV = PV \cdot (1 + r)^N + PMT \cdot \left(\frac{(1 + r)^N - 1}{r}\right)
\]
where \(r\) is the annual interest rate.
Step 3: Solve for the Interest Rate
Using the values provided, we solve the equation for \(r\). The calculated interest rate is:
\[
r \approx -1.1333
\]
Step 4: Convert to Percentage
To express the interest rate as a percentage, we multiply by 100:
\[
\text{Interest Rate} \approx -113.33\%
\]
Final Answer
The interest rate earned on Ray's investment is \(\boxed{r = -113.33\%}\).