An SME must pay the amount of $240,000 within six years. To ensure payment, the accountant proposes, given that there is liquidity in the company, to accumulate a fund through annual deposits to an account that pays 8% annually. How much should the deposits be?

Answer 1

To find out how much the annual deposits should be, we can use the future value formula for annuities:

\[ FV = P \times \left( \frac{(1+r)^n -1}{r} \right) \]

Where:
- \(FV\) is the future value of the annuity (which is $240,000)
- \(P\) is the annual deposit
- \(r\) is the annual interest rate (8% or 0.08)
- \(n\) is the number of years (6)

Substitute the values into the formula:

\[ 240,000 = P \times \left( \frac{(1+0.08)^6 - 1}{0.08} \right) \]

\[ 240,000 = P \times \left( \frac{(1.08)^6 - 1}{0.08} \right) \]

\[ 240,000 = P \times \left( \frac(1.58687475 - 1}{0.08} \right) \]

\[ 240,000 = P \times \left( \frac{0.58687475}{0.08} \right) \]

\[ 240,000 = P \times 7.33593594 \]

\[ P = \frac{240,000}{7.33593594} \]

\[ P ≈ 32,707.90 \]

Therefore, the annual deposits should be approximately $32,707.90 to accumulate a fund of $240,000 in six years at an interest rate of 8% per year.