Question

A grandparent puts $5,000 into a college education fund for a grandchild. If the fund earns 2.75% annual interest compounded daily, what is the value (in dollars) of the account after 16 years? Assume all years have 365 days.

Answer 1

The value of the account after 16 years would be approximately $7,524.34.

Step-by-step explanation:

To calculate the value of the account after 16 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years. In this case, P = $5,000, r = 2.75% or 0.0275, n = 365 (since interest is compounded daily), and t = 16. Plugging in the values, we get:

A = $5,000(1 + 0.0275/365)^(365*16)

A = $5,000(1 + 0.000075)^(5,840)

A ≈ $5,000(1.000075)^5,840

A ≈ $5,000(1.504867)

A ≈ $7,524.34

Therefore, the value of the account after 16 years would be approximately $7,524.34.