Question

Write the following as a function f(t)=a•b^t round to the nearest hundredth if necessary. you deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly

Answer 1

To have $10,000 in ten years in a bank account with 10% interest compounded annually, you would need to deposit approximately $3,855.03.

Step-by-step explanation:

Calculating the Initial Deposit for Compound Interest

To determine how much money you would need to deposit into a bank account that pays 10% interest compounded annually in order to have $10,000 in ten years, you use the formula for compound interest:

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

Where:

• P is the principal amount (initial deposit)
• 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 number of years the money is invested or borrowed for

In this case, since the interest is compounded annually, n = 1. Therefore, the formula simplifies to:

P = A / (1 + r)^t

Plugging in the known values:

P = $10,000 / (1 + 0.10)^10 = $10,000 / (1.10)^10

Calculating the denominator we get:

P = $10,000 / 2.59374

And finally, solving for P gives:

P = $3,855.03

Therefore, you would need to deposit approximately $3,855.03 into the bank account.