How much must be deposited in a bank with a 10% interest rate to realize $10,000 in 4 years?

How much must be deposited in a bank with a 10% interest rate to realize $10,000 in 4 years?

• A. $40,000
• B. $9,077
• C. $6,830
• D. $2,500

Answer: (C)

To determine how much needs to be deposited in a bank today to realize $10,000 in 4 years at a 10% interest rate, you can use the formula for present value, which takes future value and discount rates into consideration. The formula is as follows: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - PV = Present Value (the amount to be invested today) - FV = Future Value (the amount desired in the future, which in this case is $10,000) - r = interest rate (expressed as a decimal, so 10% is 0.10) - n = number of periods (in this context, the number of years, which is 4) Plugging in the values: \[ PV = \frac{10,000}{(1 + 0.10)^4} \] \[ PV = \frac{10,000}{(1.10)^4} \] \[ PV = \frac{10,000}{1.4641} \] \[ PV \approx 6,830.11 \] Thus, approximately $6,830 must be deposited today in order

To determine how much needs to be deposited in a bank today to realize $10,000 in 4 years at a 10% interest rate, you can use the formula for present value, which takes future value and discount rates into consideration. The formula is as follows:

[ PV = \frac{FV}{(1 + r)^n} ]

Where:

• PV = Present Value (the amount to be invested today)

• FV = Future Value (the amount desired in the future, which in this case is $10,000)

• r = interest rate (expressed as a decimal, so 10% is 0.10)

• n = number of periods (in this context, the number of years, which is 4)

Plugging in the values:

[

PV = \frac{10,000}{(1 + 0.10)^4}

]

[

PV = \frac{10,000}{(1.10)^4}

]

[

PV = \frac{10,000}{1.4641}

]

[

PV \approx 6,830.11

]

Thus, approximately $6,830 must be deposited today in order