Question

How much would you need to deposit in an account now in order to have $3000 in the account in 10 years? Assume the account earns 8% interest compounded quarterly. Round your answer to the nearest cent.

Answer 1

Final answer:

To have $3,000 in 10 years at an 8% interest rate compounded quarterly, one would need to deposit approximately $1,359.14 today. This is calculated using the present value formula for compound interest.

Step-by-step explanation:

To determine how much you would need to deposit in an account now to have $3,000 in the account in 10 years with an interest rate of 8% compounded quarterly, you can use the formula for the present value of a future sum in compound interest:

PV = FV / (1 + r/n)nt

Where:

• PV = Present Value (the amount to deposit now)
• FV = Future Value (the amount you want to have in the future, which is $3,000)
• r = annual interest rate (8% or 0.08 as a decimal)
• n = number of times the interest is compounded per year (quarterly compounding means 4 times per year)
• t = number of years the money is invested (10 years)

Plug in the values to the formula:

PV = 3000 / (1 + 0.08/4)4*10

Now, calculate the denominator:(1 + 0.08/4)4*10 = (1 + 0.02)40

Calculate the present value:

PV = 3000 / (1.02)40

Using a calculator, the present value comes out to approximately:

PV ≈ 3000 / 2.20804 ≈ $1359.14

Therefore, to have $3,000 in 10 years at an 8% interest rate compounded quarterly, you would need to deposit approximately $1,359.14 today.

Answer 2

We can use the formula for compound interest to solve this problem:

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

where A is the amount of money in the account after t years, P is the principal (the initial amount deposited), r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

We want to find the amount of money that needs to be deposited now (P) in order to have $3000 in the account after 10 years, so we can rearrange the formula to solve for P:

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

Plugging in the given values, we get:

P = 3000 / (1 + 0.08/4)^(4*10)

P = 3000 / 2.208756...

P = $1358.39 (rounded to the nearest cent)

Therefore, you would need to deposit $1358.39 in the account now in order to have $3000 in the account in 10 years at an 8% interest rate compounded quarterly.

*IG: whis.sama_ent*