The following incoming payments show up at a tax inspection: 25 000€ on 19.01.2008, 140 000€ on 27.03.2008 and 19 000€ on a date that which is illegible, and 60 000€ on 15.06.2008. On which date did the payment of the 19 000€ appear, if on 30.06.2008 the money on the account (incl. interest at 4%) is 246 088.89€? Use simple interest and 30E/360 DCC. Solution: 45 days, 15.05.08

To find the date that the payment of 19,000€ appeared, we can use the simple interest formula:

A = P \left( 1 + \frac{rt}{n} \right)

Where:

- A is the final amount (246,088.89€)
- P is the initial amount (the sum of all incoming payments before the 19,000€)
- r is the interest rate (4%)
- t is the time in years (the number of days from the unknown date to 30.06.2008, i.e., 45 days)
- n is the number of compounding periods per year (30E/360 DCC)

First, let's calculate the initial amount P :

P = 25,000€ + 140,000€ + 60,000€ = 225,000€

Now, let's substitute the known values into the formula and solve for t :

246,088.89€ = 225,000€ \left( 1 + \frac{0.04t}{30} \right)

Simplifying the equation, we have:

\frac{246,088.89€}{225,000€} = 1 + \frac{0.04t}{30}

1.0930711 = 1 + \frac{0.04t}{30}

Subtracting 1 from both sides:

0.0930711 = \frac{0.04t}{30}

Now, let's solve for t :

t = \frac{0.0930711 \times 30}{0.04}

t = 69.9533

Since t represents the number of days, we can round it to the nearest whole number, which is 70 days.

Therefore, the payment of 19,000€ appeared 70 days before 30.06.2008.

To find the date, we subtract 70 days from 30.06.2008:

\text{Date} = \text{30.06.2008} - \text{70 days} = \text{15.05.2008}

Answer: The payment of 19,000€ appeared on 15.05.2008.