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Your bank pays interest, compounded semiannually.find the future
value (in ) of deposited at the beginning of every six months,
for 16 years. (Round your answer to the nearest cent.)

Ask by Pierce Reeves. in the United States

Mar 21,2025

Question

File Edit Format View Help
Your bank pays interest, compounded semiannually.find the future
value (in ) of deposited at the beginning of every six months,
for 16 years. (Round your answer to the nearest cent.)

Ask by Pierce Reeves. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

We are given:
- A periodic deposit of $$ R = \$500 $$ every six months.
- An annual interest rate of $$ 4\% $$ compounded semiannually, so the interest rate per period is 
  $$
  i = \frac{4\%}{2} = 0.02.
  $$
- The investment period is 16 years. Since deposits are made semiannually, the number of periods is
  $$
  n = 16 \times 2 = 32.
  $$
- Deposits occur at the beginning of each period (annuity due).

The future value $$ FV $$ of an annuity due is given by:
$$
FV = R \times \frac{(1+i)^n - 1}{i} \times (1+i).
$$

Substitute the known values:
$$
FV = 500 \times \frac{(1.02)^{32} - 1}{0.02} \times 1.02.
$$

Step 1. Compute $$(1.02)^{32}$$:
$$
(1.02)^{32} \approx 1.8847.
$$

Step 2. Compute $$(1.02)^{32} - 1$$:
$$
1.8847 - 1 = 0.8847.
$$

Step 3. Divide by the periodic rate:
$$
\frac{0.8847}{0.02} \approx 44.235.
$$

Step 4. Multiply by the deposit amount and then by $$1.02$$:
$$
500 \times 44.235 \approx 22,\!117.5,
$$
$$
22,\!117.5 \times 1.02 \approx 22,\!559.85.
$$

Thus, the future value is approximately:
$$
\boxed{\$22,\!559.85}.
$$
The future value of the investment is approximately \$22,559.85.

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Your bank pays interest, compounded semiannually.find the future
value (in ) of deposited at the beginning of every six months,
for 16 years. (Round your answer to the nearest cent.)

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File Edit Format View Help Your bank pays interest, compounded semiannually.find the future value (in ) of deposited at the beginning of every six months, for 16 years. (Round your answer to the nearest cent.)

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File Edit Format View Help
Your bank pays interest, compounded semiannually.find the future
value (in ) of deposited at the beginning of every six months,
for 16 years. (Round your answer to the nearest cent.)