Question

Необхідно визначити теперішню вартість коштів, що вкладаються на депозитний рахунок на термін 2 роки, за таких умов: очікувана майбутня вартість коштів становить 100 000 грн., реальна процентна ставка з урахуванням інфляції – 20%, прогнозований річний темп інфляції – 12%. Інвестор планує вкладати $2000 в ануїтет на початку кожного року впродовж 3 років. Якщо проценти нараховуються щорічно в розмірі 12%, визначте суму, яку отримає цей інвестор через 5 років.

Answer 1

Ответ:

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Answer 2

Calculation of Present Value

To determine the present value of the funds invested in a deposit account for a period of 2 years, we need to take into account the expected future value of the funds, the real interest rate, and the projected annual inflation rate.

The expected future value of the funds is given as 100,000 грн. The real interest rate, which takes into account inflation, is 20%. The projected annual inflation rate is 12%.

To calculate the present value, we can use the formula for present value of a future sum of money:

Present Value = Future Value / (1 + Real Interest Rate) ^ Number of Years

In this case, the number of years is 2.

Let's calculate the present value:

Present Value = 100,000 грн / (1 + 0.20) ^ 2

Using a calculator, the present value is approximately 69,444.44 грн.

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Calculation of Investment Returns

Next, let's calculate the amount that the investor will receive after 5 years if they invest $2000 annually in an annuity for 3 years, with interest compounded annually at a rate of 12%.

To calculate the future value of an annuity, we can use the formula:

Future Value = Payment * [(1 + Interest Rate) ^ Number of Years - 1] / Interest Rate

In this case, the payment is $2000, the interest rate is 12%, and the number of years is 3.

Let's calculate the future value of the annuity:

Future Value = $2000 * [(1 + 0.12) ^ 3 - 1] / 0.12

Using a calculator, the future value of the annuity is approximately $7,254.55.

To calculate the total amount the investor will receive after 5 years, we need to add the future value of the annuity to the present value of the funds invested in the deposit account:

Total Amount = Present Value + Future Value

Total Amount = 69,444.44 грн + $7,254.55

Using a currency converter, the total amount the investor will receive after 5 years is approximately 86,699.99 грн.

Please note that currency conversion rates may vary, so the actual amount received may differ slightly.

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