# Solution:

1) With annual capitalization of the deposit, interest is accrued on the amount including already accumulated interest. In this case:

$500000 *(1.07^5)=701275.87$ rubles.

Profit from the deposit: 701275.87-500000=201275.87 rubles.

2) Without capitalization, interest is accrued on a fixed deposit amount. In this case: $500000+500000 * 0.08 * 5=700000$ rubles.

Profit from the deposit: 700000-500000=200000 rubles.

3) Cost of bars including VAT: $2350 * 1.2=2820$ rubles

Maximum amount of gold for 500000 rubles: 500000/2820=177.305 g.

Cost of gold in 5 years: $2350 * 1.6=3760$ rubles per g.

Total cost of all purchased gold in 5 years: 3760*177.305=666666.8 rubles.

Profit from the purchase: 666666.8-500000=166666.8 rubles.

4) Cost of items including VAT and markup: $31 * 1.2+31 * 0.09=39.9$ rubles

Maximum amount of silver in items for 500000 rubles: 500000/39.9=12531.328 g.

Cost of silver in 5 years: $31 * 1.7=52.7$ rubles per g.

Total cost of all silver in 5 years: 52.7*12531.328=660400.986 rubles.

Maximum profit if silver is sold at market price: 660400.986-500000=160400.986 rubles. If the scrap price is lower than the market price, the profit will be less than the calculated amount.

5) Purchase of shares: 500000/500=1000 shares.

Dividends: $400 * 1000 * 0.05 * 5=100000$ rubles

Price of 1000 shares in 5 years: 500000+500000*0.18=590000 rubles.

Profit from selling shares in 5 years: 590000+100000-500000=190000 rubles.

Thus, the most profitable option is option 1).

## Grading Criteria:

- Full correct solution of point 1) - 2 points. If the profit is not calculated, only 1 point for the solution.
- Full correct solution of point 2) - 2 points. If the profit is not calculated, only 1 point for the solution.
- Full correct solution of point 3) - 5 points. Of which, VAT is correctly accounted for 2 points, the amount of gold is correctly found - 1 point, the cost in 5 years is correctly found - 1 point, the profit is correctly calculated - 1 point.
- Full correct solution of point 4) - 6 points. Of which, VAT is correctly accounted for 1 point, the store markup is correctly accounted for - 1 point, the amount of silver is correctly found - 1 point, the cost per gram in 5 years is correctly found - 1 point, the total cost of silver is correctly calculated - 1 point, the profit is correctly calculated - 1 point.
- Full correct solution of point 5) - 5 points. Of which, the number of shares is correctly found - 1 point, dividends are correctly found - 1 point, the share price in 5 years is correctly found - 1 point, the sale price of shares in 5 years is correctly calculated - 1 point, the profit is correctly calculated - 1 point.
- Arithmetic errors are penalized by reducing the score by 1 point.
Task 2.

The son of Lieutenant Schmidt received an inheritance of 500,000 rubles and decided that it would be prudent to invest this money. Consulting a financial advisor with the gift of clairvoyance, the son of Lieutenant Schmidt learned about the following investment opportunities:

1) deposit the money in the "Flying Dutchman" bank with annual capitalization at an annual interest rate of $7 \%$ for 5 years;
2) deposit the money in the "Flying Dutchman" bank without capitalization at an annual interest rate of $8 \%$ for 5 years;
3) invest the money in gold bars, considering that the price of gold will increase by 1.6 times over 5 years (the cost of 1 g of gold $=2350$ rubles, include VAT when purchasing bars from the bank);
4) invest the money in silver jewelry, considering that the price of silver will increase by 1.7 times over 5 years (the cost of 1 g of silver $=31$ rubles, include VAT and a store markup of $9 \%$ of the cost of silver), with the plan to pawn the items at the pawnshop for the scrap value;
5) invest the money in shares of the construction company "PenoBlok," considering that the share price will increase by $18 \%$ over 5 years (shares with a nominal value of 400 rubles and a market value of 500 rubles, dividends $=5 \%$ per year).

Calculate the profit from each of the proposed investments and determine which one will be the most profitable for the son of Lieutenant Schmidt.