Question

Sylvia wants to go on a cruise in 3 years. She could earn 5.2 percent compounded monthly in a bank account if she were to deposit the money today. She needs to have 9,000 dollars in 3 years. How much will she have to deposit today?

Answer 1

Sylvia should deposit approximately $7,743.51 into a savings account to reach her $9,000 goal in 3 years with a 5.2% interest rate compounded monthly.

Step-by-step explanation:

To calculate the initial deposit Sylvia needs to make to have $9,000 in 3 years with an interest rate of 5.2% compounded monthly, we'll use the formula for compound interest: P = A / (1 + r/n)^(nt), where:

• P is the initial principal (the amount of money to deposit today).
• A is the future value of the investment/loan, including interest ($9,000 in this case).
• 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 the money is invested for.

First, convert the annual interest rate from a percentage to a decimal by dividing by 100: 5.2% / 100 = 0.052.
Since the interest is compounded monthly, n is 12.
t is 3 years.
Thus, we have: P = 9000 / (1 + 0.052/12)^(12*3).
Upon calculating, P equals approximately $7,743.51. This is the amount Sylvia needs to deposit today.

is that Sylvia needs to deposit approximately $7,743.51 today in order to have $9,000 in 3 years, assuming a 5.2% interest rate compounded monthly.