Question

expect their sales to increase by 4% each year over the next three yeacs. Company Y invests inte an accnunt earning an APR, of 1.3% compounded continuoust. Assume a continobub incume atreami How much money wial be in the investment account on Deceenber 31,2020? Mound wour answer to three decimal places. bilition doitars How much money dld Corrpany if inyest in the account between january 4,2018 and Deceriner 31,2020 ? Round vour answer to three decimal places. bilion dokicars Hew much unterest did Company Y earn on.this inveitment botween lanuary 1, 201 and December, 31.2020 binich doliars

Answer 1

The balance in Company Y's investment account on December 31, 2020, will be $1,048.62 million.

Step-by-step explanation:

Company Y expects a 4% annual increase in sales for the next three years. This translates to a compound annual growth rate (CAGR) of 4%. Using the compound interest formula, we can calculate the future value of the investment:

FV = PV * (1 + r/n)^(n * t)

PV = initial investment, r = annual interest rate (APR / 12), n = number of times interest is compounded per year (continuous compounding), t = number of years.

Let's assume Company Y invested $1 billion on January 1, 2018. The APR is 1.3%, which is equivalent to an annual interest rate of 0.11%. Since interest is compounded continuously, n is infinite. Therefore, the formula simplifies to:

FV = PV * e^(r * t)

FV = $1 billion * e^(0.0011 * 3)

FV = $1,048.62 million

The investment will grow to $1,048.62 million by December 31, 2020.

Now let's calculate the total amount invested between January 4, 2018, and December 31, 2020. We can use the present value formula to find the present value of the future cash flows:

PV = FV / (1 + r/n)^(n * t)

Let's assume Company Y did not withdraw any money from the account during this period. The future value on December 31, 2020, is $1,048.62 million as calculated earlier. The number of years and times interest is compounded per year are both three since we are calculating the present value between January 4, 2018, and December 31, 2020. Therefore:

PV = $1,048.62 million / (1 + 0.0011)^(3 * 3)

PV = $999.97 million

This means that Company Y invested approximately $999.97 million between January 4, 2018, and December 31, 2020. The exact amount invested during this period may be different due to fluctuations in sales and other factors that may have affected the company's cash flows during this period. However, assuming no withdrawals or additional investments during this period, our calculation provides a reasonable estimate of the total amount invested during this period based on the given information.