Questions: The Ramirez family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 7.8% interest, compounded monthly. Payments will be made at the end of each month. How much money do they need to pay into the annuity each month for the annuity to have a total value of 14,000 after 10 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

The Ramirez family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 7.8% interest, compounded monthly. Payments will be made at the end of each month. How much money do they need to pay into the annuity each month for the annuity to have a total value of 14,000 after 10 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.
Transcript text: The Ramirez family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns $7.8 \%$ interest, compounded monthly. Payments will be made at the end of each month. How much money do they need to pay into the annuity each month for the annuity to have a total value of $\$ 14,000$ after 10 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. s! $\square$
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Solution

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Solution Steps

Step 1: Identify the Parameters

The future value (FV) desired is $14000, the annual interest rate (r) is 7.8%, the time (t) is 10 years, and the number of compounding periods per year (n) is 12.

Step 2: Apply the Periodic Payment Formula

The formula to calculate the periodic payment \(P\) for an ordinary annuity is: \[P = \frac{FV \times r/n}{(1 + r/n)^{nt} - 1}\] Substitute the given values into the formula: \[P = \frac{14000 \times 0.078/12}{(1 + 0.078/12)^{12*10} - 1}\]

Step 3: Calculate the Periodic Payment

After substituting the values, the periodic payment \(P\) is calculated to be $77.38.

Final Answer:

The periodic payment needed to reach a future value of $14000 in 10 years with an annual interest rate of 7.8% compounded monthly is approximately $77.38.

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