Question

At the end of year 3, the account was valued at $1674.58. At the end of year 4, the account was valued at $1739.89. What was the value of the account at the end of year 33? Round your answer to the nearest whole number.

Answer 1

To find the value of the account at the end of year 33, we can use the process of accumulating interest. By finding the annual interest rate, we can determine the value at the end of year 33. The value of the account at the end of year 33 is $2418.

Step-by-step explanation:

To find the value of the account at the end of year 33, we can consider the process of accumulating interest. Let's assume that the account has been growing at a constant interest rate. To find this rate, we can divide the value at the end of year 4 by the value at the end of year 3: (1739.89 / 1674.58) = 1.039. This means that the value of the account has increased by 3.9% each year. To find the value at the end of year 33, we multiply the value at the end of year 3 by (1.039)^30 (since 33 - 3 = 30): 1674.58 * (1.039)^30 = 2417.58.

Answer 2

The value of the account at the end of year 33 is $5024. Round it to the nearest whole number.

Step-by-step explanation:

To find the value of the account at the end of year 33, we can use the concept of exponential growth or decay. Assuming this is a situation of compound interest, where the value grows over time, we can use the formula for compound interest:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

Where:

• A is the ending balance,
• P is the principal amount (initial value of the account),
• r is the annual interest rate (as a decimal),
• n is the number of times interest is compounded per year,
• t is the number of years.

Given the values for the end of year 3 and year 4, we can set up two equations using the formula and solve for the principal amount. Then, using the same formula, we can find the value at the end of year 33.

After obtaining the principal amount, substitute \( t = 33 \) into the formula to find the value of the account at the end of year 33. Round the result to the nearest whole number, as specified in the question.

In conclusion, by applying the compound interest formula and utilizing the given values, we can determine the value of the account at the end of year 33.