Question

An account is opened with an initial deposit of $2,500 and earns 1.8% interest compounded semi-annually. What will the account be worth in 30 years? Round your answer to the nearest cent.

Answer 1

To calculate the future value of an account with compound interest, we can use the formula A = P(1 + r/n)^(nt). In this case, the account with an initial deposit of $2,500 and an annual interest rate of 1.8% compounded semi-annually will be worth approximately $4,386.92 after 30 years.

Step-by-step explanation:

To calculate the future value of an account with compound interest, we can use the formula:

`A = P(1 + r/n)^(nt)`

Where:

• A is the future value of the account
• P is the initial deposit
• r is the annual interest rate
• n is the number of times the interest is compounded per year
• t is the number of years

In this case, we have:

• P = $2,500
• r = 1.8% or 0.018
• n = 2 because interest is compounded semi-annually
• t = 30 years

Substituting these values into the formula:

`A = 2500(1 + 0.018/2)^(2*30)`

Calculating this expression, the account will be worth approximately $4,386.92 after 30 years.

Answer 2

The account will be worth $5,822.20 in 30 years

Step-by-step explanation:

To calculate the value of the account after 30 years, we need to use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $2,500, the interest rate is 1.8%, interest is compounded semi-annually (n=2), and the number of years is 30.

Plugging in these values into the formula, we get: A = 2,500(1+0.018/2)^(2*30) = $5,822.20.

Therefore, the account will be worth $5,822.20 in 30 years.