Question

Find how much money should be deposited in a bank paying interest at the rate of 5.5%/ year compounded quarterly so that at the end of 3 years, the accumulated amount will be $90,000. (Round your answer to the nearest cent.)

Answer 1

To accumulate $90,000 in three years in an account with a 5.5% interest rate compounded quarterly, approximately $75,874.67 must be initially deposited.

Step-by-step explanation:

To find out how much needs to be deposited in a bank paying a compound interest rate of 5.5% per year, compounded quarterly, to have $90,000 at the end of 3 years, we use the formula for compound interest:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount deposited).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is deposited for, in years.

We want to find P when A = $90,000, r = 0.055 (because 5.5% = 5.5/100 = 0.055), n = 4 (because the interest is compounded quarterly), and t = 3.

The formula becomes:

$90,000 = P(1 + 0.055/4)(4*3)

Now we solve for P:

$90,000 = P(1 + 0.01375)12

$90,000 = P(1.01375)12

P = $90,000 / (1.01375)12

Using a calculator:

P ≈ $90,000 / 1.186384

P ≈ $75,874.67

Therefore, approximately $75,874.67 should be deposited to have $90,000 in three years.