How much should be deposited into an account today if it is to accumulate to $32400 in 30 years if the account bears interest at 8.01% compounded monthly?
I did A = 32400(1 + 0.0801/12)^(12*30) = $355,375, but that's wrong...
you figured how much will be there in 30 years if 32400 is deposited now. You want
A(1 + 0.0801/12)^(12*30) = 32400
A = 2953.95
thanks!
To calculate how much should be deposited into the account today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (in this case, $32,400)
P = the principal amount (the amount to be deposited today)
r = the annual interest rate (in decimal form, 8.01% becomes 0.0801)
n = the number of times interest is compounded per year (monthly compounding, so n = 12)
t = the number of years the money is invested for (30 years)
Let's rewrite the formula using the known values:
32400 = P(1 + 0.0801/12)^(12*30)
Now, to solve for P, we need to isolate it. First, let's simplify the exponent:
32400 = P(1.006675)^360
Next, divide both sides of the equation by (1.006675)^360:
32400 / (1.006675)^360 = P
Using a calculator, we can evaluate (1.006675)^360 to get approximately 4.590847. Now, divide 32400 by this value to find P:
P = 32400 / 4.590847 ≈ $7,055.04
So, approximately $7,055.04 should be deposited into the account today in order for it to accumulate to $32,400 in 30 years with an interest rate of 8.01% compounded monthly.