QuestionJuly 21, 2025

Aiko estimates she will need 35,000 for a new computerized office system. Aiko decides to put aside the money today so that it will be available in 10 years. Pod Bank offers her 8% interest compounded semiannually. How much must Aiko invest today to have 35,000 in 10 years? Aiko invest square

Aiko estimates she will need 35,000 for a new computerized office system. Aiko decides to put aside the money today so that it will be available in 10 years. Pod Bank offers her 8% interest compounded semiannually. How much must Aiko invest today to have 35,000 in 10 years? Aiko invest square
Aiko estimates she will need 35,000 for a new computerized office system. Aiko decides to put aside the money today so that it will
be available in 10 years. Pod Bank offers her 8%  interest compounded semiannually. How much must Aiko invest today to have
 35,000 in 10 years?
Aiko invest square

Solution
4.3(204 votes)

Answer

Aiko must invest approximately \15,974.87. Explanation 1. Identify the formula for compound interest Use the formula for future value with compound interest: **FV = PV \times (1 + \frac{r}{n})^{nt}**. 2. Define variables FV = 35000, r = 0.08, n = 2, t = 10. 3. Rearrange the formula to solve for present value (PV) **PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}**. 4. Calculate the present value Substitute the values: PV = \frac{35000}{(1 + \frac{0.08}{2})^{2 \times 10}}. 5. Compute the result PV = \frac{35000}{(1.04)^{20}} \approx \frac{35000}{2.191123}.

Explanation

1. Identify the formula for compound interest<br /> Use the formula for future value with compound interest: **$FV = PV \times (1 + \frac{r}{n})^{nt}$**.<br /><br />2. Define variables<br /> $FV = 35000$, $r = 0.08$, $n = 2$, $t = 10$.<br /><br />3. Rearrange the formula to solve for present value (PV)<br /> **$PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$**.<br /><br />4. Calculate the present value<br /> Substitute the values: $PV = \frac{35000}{(1 + \frac{0.08}{2})^{2 \times 10}}$.<br /><br />5. Compute the result<br /> $PV = \frac{35000}{(1.04)^{20}} \approx \frac{35000}{2.191123}$.
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