Question

The Petersons are saving up for a family vacation in 2 years. They invest $2700 in an account with an annual interest rate of 1.15%, compounded daily. Determine the amount in their account after 2 years and the interest earned on their investment.

Answer 1

The amount in the Petersons' account after 2 years is approximately $2760.89, and the interest earned on their investment is $60.89.

Step-by-step explanation:

To determine the amount in the Petersons' account after 2 years and the interest earned, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal investment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal investment is $2700, the annual interest rate is 1.15%, and the interest is compounded daily (n = 365). Plugging in these values, we have:

A = 2700(1 + 0.0115/365)^(365*2)

Simplifying the equation, we find that the amount in the Petersons' account after 2 years is approximately $2760.89. To determine the interest earned, we subtract the principal investment from the final amount:
Interest Earned = $2760.89 - $2700 = $60.89