Question

How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns 8% interest compounded monthly. Use the compound interest formula a=p(1+r/n)^nt

to solve for the initial deposit.

Answer 1

To have $3000 in 15 years at an 8% interest rate compounded monthly, one would need to initially deposit approximately $886.49. This calculation is done using the compound interest formula rearranged to solve for the principal amount.

Step-by-step explanation:

To figure out how much you need to deposit now to have $3000 in 15 years at an 8% interest rate compounded monthly, we start with the compound interest formula:

a = p(1 + r/n)^(nt)

Where:

• a is the amount we want to have in the future, which is $3000.
• p is the principal amount, or the initial deposit we're solving for.
• r is the annual interest rate (in decimal form, 8% is 0.08).
• n is the number of times interest is compounded per year, which is 12 for monthly compounding.
• t is the number of years, which is 15.

We rearrange the formula to solve for p:

p = a / (1 + r/n)^(nt)

Plugging in our values:

p = 3000 / (1 + 0.08/12)^(12*15)

Now we do the calculation:

p = 3000 / (1 + 0.0066667)^(180)

p = 3000 / (1.0066667)^(180)

p ≈ 3000 / 3.386035

p ≈ 886.49

You would need to deposit approximately $886.49 now in order to have $3000 in the account in 15 years with an 8% interest rate compounded monthly.