Jse 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.)

Ask by Herrera Ortiz. in the United States

Mar 21,2025

Question

Jse 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.)

Ask by Herrera Ortiz. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

Let

- $$ P = 300 $$ (the amount deposited every six months),
- The nominal annual interest rate is $$ 4\% $$. Since interest is compounded semiannually, the effective rate per deposit period is 
  $$
  i = \frac{4\%}{2} = 0.02.
  $$
- The total number of deposit periods in 17 years is 
  $$
  n = 17 \times 2 = 34.
  $$

Because deposits are made at the beginning of each period, we are dealing with an annuity due. The future value ($$ FV $$) of an annuity due is given by

$$
FV = P \cdot \frac{(1+i)^n - 1}{i} \cdot (1+i).
$$

Substitute the values:

$$
FV = 300 \cdot \frac{(1.02)^{34} - 1}{0.02} \cdot 1.02.
$$

Now, compute step by step:

1. Compute $$(1.02)^{34}$$.

Using logarithms or a calculator, we find

$$
   (1.02)^{34} \approx 1.960.
   $$

2. Subtract 1:

$$
   (1.02)^{34} - 1 \approx 1.960 - 1 = 0.960.
   $$

3. Divide by $$ i $$:

$$
   \frac{0.960}{0.02} = 48.
   $$

4. Multiply by $$ P $$ and then by $$1.02$$:

$$
   300 \times 48 = 14,\!400,
   $$
   $$
   14,\!400 \times 1.02 \approx 14,\!688.
   $$

Thus, the future value is approximately

$$
\boxed{\$14,\!688.00}.
$$
The future value is approximately \$14,688.00.

Jse 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.)

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Jse 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.)

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preguntas relacionadas

Latest Economics Questions

Jse 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.)