Question

How much money should be deposited today in an account that earns 5.81% compounded daily so that it will accumulate to $6,200 in 8 years?

Use this formula:
PV=FV/(1+r/n)^nt



Enter the dollar amount rounded up to the nearest cent.

Your Answer:

Answer 1

To calculate the present value (PV), we can use the formula provided:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- \( FV \) is the future value ($6,200 in this case)
- \( r \) is the annual interest rate (5.81% or 0.0581)
- \( n \) is the number of times the interest is compounded per year (daily, so \( n = 365 \))
- \( t \) is the number of years (8 years)

Now, let's substitute the values into the formula:

1. Calculate \( r/n \):
\[
r/n = \frac{0.0581}{365} \approx 0.000159452
\]

2. Calculate \( nt \):
\[
nt = 365 \times 8 = 2920
\]

3. Now plug in the values into the formula:
\[
PV = \frac{6200}{(1 + 0.000159452)^{2920}}
\]

4. Calculate \( (1 + 0.000159452)^{2920} \):
\[
(1 + 0.000159452)^{2920} \approx 1.199856982
\]

5. Now calculate the present value:
\[
PV = \frac{6200}{1.199856982} \approx 5163.49
\]

Therefore, the amount that should be deposited today is approximately **$5,163.49**.

Rounded to the nearest cent, the answer is:

**$5,163.49**.