Question

Lauren invested 510 in an account in the year 2010, and the value has been growing exponentially at a constant rate. The value of the account reached620 in the year 2014. Determine the value of the account in the year 2016?

Answer 1

The question involves calculating exponential growth of an account based on given values. Solving for the growth rate using values from 2010 and 2014 will allow us to predict the account's value in 2016.

Step-by-step explanation:

This question involves the concept of exponential growth. Lauren's account increases in value exponentially, and we're given two data points: the account value was $510 in 2010 and it had grown to $620 by 2014. We follow the formula for future value: Future Value = Present Value × (1 + g) ^ n, where 'g' is the growth rate and 'n' is the number of periods.

To solve for the growth rate, we'll use the provided values and solve for g in the formula: $620 = $510 × (1 + g) ^ 4. Once solved, the growth rate can be used to project the account's value in 2016 (n=6 years from 2010) using the same formula: Future Value in 2016 = $510 × (1 + g)^6.

Please note that this solution assumes the growth rate calculated based on 2010-2014 data continues unchanged for 2016.

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