Use the appropriate formula to find the future value (in ) of
deposited at the beginning of every six months, for 17 years if a bank
pays interest, compounded semiannually. (Round your answers to the
nearest cent.)
Ln 9, Col 1

Ask by Vega Ford. in the United States

Mar 21,2025

Question

Use the appropriate formula to find the future value (in ) of
deposited at the beginning of every six months, for 17 years if a bank
pays interest, compounded semiannually. (Round your answers to the
nearest cent.)
Ln 9, Col 1

Ask by Vega Ford. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

**Step 1. Identify the parameters.**  
The deposits are made at the beginning of each period (annuity due). The deposit amount is  
$$
R = \$300,
$$  
the annual interest rate is  
$$
4\%,
$$  
compounded semiannually so the interest rate per period is  
$$
i = \frac{0.04}{2} = 0.02,
$$  
and the number of periods (since there are 2 periods per year for 17 years) is  
$$
n = 17 \times 2 = 34.
$$

---

**Step 2. Write the formula for an annuity due.**  
For an annuity due, the future value is given by:
$$
FV = R \times \left(\frac{(1+i)^n - 1}{i}\right) \times (1+i).
$$

---

**Step 3. Substitute the values into the formula.**  
Substitute $$ R = 300 $$, $$ i = 0.02 $$, and $$ n = 34 $$ into the formula:
$$
FV = 300 \times \left(\frac{(1.02)^{34} - 1}{0.02}\right) \times 1.02.
$$

---

**Step 4. Calculate $$(1.02)^{34}$$.**  
Calculate the compound factor:
$$
(1.02)^{34} \approx 1.96 \quad (\text{using a calculator or logarithms}).
$$

Then:
$$
(1.02)^{34} - 1 \approx 1.96 - 1 = 0.96.
$$

---

**Step 5. Compute the future value.**  
Plug the values back into the formula:
$$
FV = 300 \times \left(\frac{0.96}{0.02}\right) \times 1.02.
$$

First, compute the fraction:
$$
\frac{0.96}{0.02} = 48.
$$

Then:
$$
48 \times 1.02 = 48.96.
$$

Finally:
$$
FV = 300 \times 48.96 \approx 14688.
$$

---

**Step 6. Write the final answer.**  
The future value of the annuity is approximately:
$$
\boxed{\$14,\!688.00}.
$$
The future value of the annuity is approximately \$14,688.00.

Use the appropriate formula to find the future value (in ) of
deposited at the beginning of every six months, for 17 years if a bank
pays interest, compounded semiannually. (Round your answers to the
nearest cent.)
Ln 9, Col 1

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Use the appropriate formula to find the future value (in ) of deposited at the beginning of every six months, for 17 years if a bank pays interest, compounded semiannually. (Round your answers to the nearest cent.) Ln 9, Col 1

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Latest Economics Questions

Use the appropriate formula to find the future value (in ) of
deposited at the beginning of every six months, for 17 years if a bank
pays interest, compounded semiannually. (Round your answers to the
nearest cent.)
Ln 9, Col 1