Question

How much must you deposit in an account today so that you have a

balance of $1,000 at the end of five years if interest on the
account is 4%, compounded quarterly?

Answer 1

To have a balance of $1,000 at the end of five years with a 4% interest rate compounded quarterly, you need to deposit approximately $819.40 today, using the compound interest formula.

Step-by-step explanation:

To determine how much must be deposited in an account today to have a balance of $1,000 at the end of five years with an interest rate of 4%, compounded quarterly, we can use the formula for compound interest:

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

Where:

• P = the present value (the amount of money you must deposit today)
• A = the future value ($1,000)
• r = the annual interest rate (0.04 for 4%)
• n = the number of times interest is compounded per year (4 for quarterly)
• t = the number of years the money is invested (5)

Plugging in the values gives us:

P = $1,000 / (1 + 0.04/4)(4*5)

P = $1,000 / (1 + 0.01)20

P = $1,000 / (1.01)20

P = $1,000 / 1.21989

P ≈ $819.40

So, you would have to deposit approximately $819.40 today to have $1,000 in your account after five years, with a 4% interest rate compounded quarterly.