Question

Find how much money should be deposited in a bank paying interest at the rate of 6.5%/year compounded quarterly so that at the end of 5 years, the accumulated amount will be $20,000. (round your answer to the nearest cent.)

Answer 1

To accumulate $20,000 at the end of 5 years with 6.5% interest compounded quarterly, approximately $14,838.94 should be deposited in the bank.

Step-by-step explanation:

To find how much money should be deposited in the bank to accumulate $20,000 at the end of 5 years with 6.5% interest compounded quarterly, we can use the formula for compound interest:

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

Where:

• A is the accumulated amount
• P is the principal amount (the amount to be deposited)
• r is the annual interest rate
• n is the number of times the interest is compounded per year
• t is the time period in years

Substituting the given values into the formula, we have:

A = P(1 + 0.065/4)^(4*5)

20000 = P(1 + 0.01625)^20

Dividing both sides by (1 + 0.01625)^20 gives:

P = 20000 / (1 + 0.01625)^20

Using a calculator, we can calculate P to the nearest cent:

P ≈ $14,838.94