The value of Yong's investment account increases at a rate that is proportional at any time to the value of the account at that time. Her account was worth $2000 initially, and it increases by 10% every 4 years. What is the value of Yong's investment account after 7 years? Choose 1 answer: (A) $2036 (B) $2350 (C) $2363

Question

The value of Yong's investment account increases at a rate that is proportional at any time to the value of the account at that time. Her account was worth  $2000 initially, and it increases by  10% every 4 years. What is the value of Yong's investment account after 7 years? Choose 1 answer: (A)  $2036 (B)  $2350 (C)  $2363

Bytelearn · Accepted Answer

Identify Growth Type: Identify the type of growth described in the problem. The problem states that the investment increases by a fixed percentage over equal time intervals, which is characteristic of exponential growth.Determine Growth Factor: Determine the growth factor for the investment. Since the account increases by 10% every 4 years, the growth factor for each 4-year period is 1 + 10/100 = 1.10.Calculate Periods in 7 Years: Calculate the number of 4-year periods in 7 years. To find out how many full 4-year periods fit into 7 years, we divide 7 by 4, which gives us 1 full period with a remainder of 3 years.Calculate Value After Period: Calculate the value of the investment after the full 4-year period. After one 4-year period, the investment will be worth $2000 * 1.10 = $2200.Determine Growth Rate: Determine the growth rate for the remaining 3 years. Since the growth is proportional to the value of the account and occurs continuously, we need to prorate the 10% growth over the 4-year period to find the growth for 3 years. This is done by raising the growth factor to the power of the fraction of the period that has passed, which is 3/4.Calculate Value After 3 Years: Calculate the value of the investment after the remaining 3 years. The investment will grow to $2200 * (1.10)^(3/4). We need to calculate (1.10)^(3/4) to find the exact value.Perform Growth Calculation: Perform the calculation for the growth over the remaining 3 years. (1.10)^(3/4) is approximately 1.077217345. Multiplying this by $2200 gives us the final value of the investment after 7 years: $2200 * 1.077217345 ≈ $2368.88.Choose Closest Answer: Choose the closest answer to the calculated value. The closest answer to $2368.88 is (C) $2363.

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