Question

Your company needs 700000 dollars in four years time for renovations and can earn 10% interest on investments. (a) What is the prêsent value of the renovations? Present value =__________________dollars (b) If your company deposits money continuously at a constant rate throughout the four-year period, at what rate should the money be deposited so that you have the 700000 dollars when you need it? Round your answers to 2 decimal places. Money deposited at á rate of ______________dollars per year.

Answer 1

To find the present value of the renovations, use the present value formula. To find the deposit rate, use the continuous deposit formula.

Step-by-step explanation:

To find the present value of the renovations, we need to calculate the amount of money needed in the present that will grow to $700000 in four years at a 10% interest rate. We can use the formula:

Present Value = Future Value / (1 + Interest rate)^Number of years

Plugging in the values, we have:

Present Value = 700000 / (1 + 0.10)^4 = $508520.73

To find the rate at which money should be deposited continuously, we can use the formula:

Rate = Ln(Future Value / Present Value) / Number of years

Plugging in the values, we have:

Rate = Ln(700000 / 508520.73) / 4 = 0.0736 dollars per year