Problem K. 223. (November 2009)

K. 223. A bank pays 6% annual interest on fixed deposits. The actual amount paid by the bank is calculated by finding the interest per day (counting 365 days per year), and multiplying by the number of days for which the deposit is fixed. When the locking period is over, the fixed amount is returned to the bank account and the interest is added. In addition, the bank sends letters to the customer informing them about the beginning and the end of the locking period. The letters cost 75 forints each. What is the minimum deposit it is worth fixing for 30 days in this bank? (The bank pays 0% interest on accounts not fixed.)

(6 pont)

Deadline expired on December 10, 2009.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A postaköltség \(\displaystyle 150 Ft\), amit a végén, vagy egy másik folyószámláról vonnak le. Ezért akkor éri meg a lekötés, ha a kapott kamat mértéke meghaladja a postaköltséget, azaz \(\displaystyle \displaystyle{\frac{30 \cdot 0,06}{365}x\ge 150}\). Így \(\displaystyle x\ge 30\ 416,\dot{6}\): legalább \(\displaystyle \mathbf{30\ 417\ Ft}\)-ot érdemes lekötni.

Statistics:

191 students sent a solution.
6 points:	118 students.
5 points:	14 students.
4 points:	7 students.
2 points:	5 students.
1 point:	2 students.
0 point:	41 students.
Unfair, not evaluated:	4 solutionss.

Problems in Mathematics of KöMaL, November 2009