Final answer:
To calculate the initial deposit required so that an account with 5.3% annual interest, compounded monthly, contains $18000 at the end of one year, the compound interest formula P = A / (1 + r/n)^(nt) is used.
Step-by-step explanation:
To determine how much must be deposited now in a bank account that pays 5.3% annual interest, compounded monthly, to have exactly $18000 at the end of one year, we use the formula for compound interest:
P = A / (1 + r/n)nt
Where:
- P is the principal amount (the initial amount of money)
- A is the future value of the investment/loan, including interest
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the time in years
In this case, A = $18000, r = 0.053, n = 12 (since the interest is compounded monthly), and t = 1 (since we are calculating for one year).
Therefore, the formula becomes:
P = $18000 / (1 + 0.053/12)12*(1)
Use a calculator to find P. This will give you the amount that needs to be deposited now to reach $18000 in one year, taking into account the monthly compound interest.