Question

How much money would you have to deposit into your savings accounttoday if your interest rate is 6% compounded quarterly, and you want tosave $12,000 over the next 3 years?

Answer 1

To have $12,000 in 3 years in a savings account with a 6% interest rate compounded quarterly, you would need to deposit approximately $10,037.21 today. This calculation is done using the formula for compound interest, considering the interest rate, the compounding frequency, and the time period.

Step-by-step explanation:

To determine how much money you would need to deposit into a savings account today to have $12,000 in 3 years at a 6% interest rate compounded quarterly, you can use the formula for compound interest:

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

where: P = the principal amount (the initial amount of money) A = the future value of the investment/loan, including interest r = the annual interest rate (decimal) n = the number of times that interest is compounded per unit t t = the time the money is invested or borrowed for, in years

In this case, A is $12,000, r is 0.06 (6% expressed as a decimal), n is 4 (since it's compounded quarterly), and t is 3 years.

So, our formula becomes: P = $12,000 / (1 + 0.06/4)(4*3)

Calculating that out, we get:

P = $12,000 / (1 + 0.015)12

P ≈ $12,000 / (1.195618643) P ≈ $10,037.21

You would need to deposit approximately $10,037.21 into your savings account today at a 6% interest rate compounded quarterly to have $12,000 in 3 years.

Answer 2

To calculate the amount to deposit today for $12,000 in 3 years at 6% interest compounded quarterly, use the formula PV = FV / (1 + r/n)^(nt). Plugging the values into the formula, you can find the present value needed to be deposited.

Step-by-step explanation:

To find out how much money you need to deposit today to have $12,000 in your savings account in 3 years with an interest rate of 6% compounded quarterly, we need to use the formula for compound interest:

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

Where:

• PV = Present Value (the amount of money you need to deposit now)
• FV = Future Value (the amount you want to have in the future, which is $12,000)
• r = annual interest rate (6% or 0.06)
• n = number of times interest is compounded per year (quarterly compounding means n=4)
• t = number of years the money is invested (3 years)

Following the formula:

PV = $12,000 / (1 + 0.06/4)(4*3)

This calculation will give us the present value we need to deposit. After plugging in the numbers, we would perform the calculation to find that amount.
This concept illustrates the power of compound interest and the advantage of starting to save money early to allow it to grow over time.