I can't seem to figure this problem out:
You make $4,800 annual deposits into a retirement account that pays 10.5 percent interest compounded monthly.
Required:
How large will your account balance be in 30 years?
I feel like I'm really close, though. Here is where I'm at so far:
F(4800)=4800*[((1-(1+(0.105/12))^360)/(1-(1+(0.105/12))]
N = 360 (or 30 yrs. * 12 mo/yr)
I = 10.5/360 = .029
PV=0
PMT=-4800/yr
I don't get what I'm doing wrong and there aren't really any references provided in class to work off of.
You're on the right track! It seems like you're using the formula for the future value of an ordinary annuity correctly. However, there are a couple of mistakes in your calculation.
First, the interest rate per period should be the annual interest rate divided by the number of compounding periods per year. In this case, since the interest is compounded monthly, you should divide the annual interest rate of 10.5% by 12. So, the interest rate per period (i) should be 0.105/12 = 0.00875.
Next, I see that you have correctly identified that the number of periods (n) is 360 (30 years multiplied by 12 months per year for monthly compounding).
Now let's correct the formula. The future value of an ordinary annuity formula is:
FV = PMT * [((1 + i)^n - 1) / i]
Using the values you've given:
PMT = -4800 (negative because it's a cash outflow, or deposit)
i = 0.00875 (monthly interest rate)
n = 360 (number of months)
Plugging in these values, the corrected formula would be:
FV = -4800 * [((1 + 0.00875)^360 - 1) / 0.00875]
Calculating this expression will give you the account balance after 30 years. Using a calculator or a spreadsheet software, evaluate the expression to find the answer.
Note: Make sure the interest rate and compounding period align with the formula you are using. Different formulas may have variations in how they handle interest rates and compounding periods.