Question

How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $6,000 after 30 years and 6 months?

Enter the answer in dollars and cents, and round to the nearest cent, if needed.

Principle = $___

Answer 1

To find out how much should be deposited in an account to have a balance of $6,000 after 30 years and 6 months with a 4.5% interest rate compounded semiannually, you can use the compound interest formula:

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

Where:

A = the future balance ($6,000 in this case)

P = the principal amount you want to find

r = the annual interest rate (4.5% or 0.045 as a decimal)

n = the number of times the interest is compounded per year (semiannually means 2 times per year)

t = the number of years (30 years and 6 months, which is 30.5 years)

Now, plug in the values and solve for P:

$6,000 = P(1 + 0.045/2)^(2 * 30.5)

$6,000 = P(1 + 0.0225)^(61)

$6,000 = P(1.0225)^61

To solve for P, divide both sides by (1.0225)^61:

P = $6,000 / (1.0225)^61

Now, calculate P:

P ≈ $2,268.45 (rounded to the nearest cent)

So, you would need to deposit approximately $2,268.45 to have a balance of $6,000 after 30 years and 6 months, with a 4.5% interest rate compounded semiannually.

Answer 2

So, you should deposit approximately $2,535.68 in the account to have a balance of $6,000 after 30 years and 6 months when compounded semiannually.