to establish a college fun, what lump sum must be deposited in order to have $30,000.00 in the fund at the end 0f 15 years? Assume a 7.5% interest rate, compounded monthly
30000 = x [1 + (.075 / 12)]^(15 * 12)
log(30000) = log(x) + 180 log(1.0625)
log(30000) = log(x) + 180 log(1.0625)
should read: log(30000) = log(x) + 180 log(1.00625)
or
from the first line
300000 = x(1.00625)^180
x = 30000/1.00625^180 = 9773.73
The log equations yields the same result.
oops...decimal place
sorry about that
To determine the lump sum that needs to be deposited in order to have $30,000.00 in the college fund at the end of 15 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount in the fund ($30,000.00 in this case)
P is the principal amount (the initial deposit)
r is the annual interest rate (7.5% or 0.075 in decimal form)
n is the number of times the interest is compounded per year (monthly compounding, so n = 12)
t is the number of years (15 years in this case)
Plugging in the values we know, we can solve for P:
$30,000.00 = P(1 + 0.075/12)^(12*15)
To simplify the equation, we can divide both sides by (1 + 0.075/12)^(12*15):
P = $30,000.00 / (1 + 0.075/12)^(12*15)
Now, let's calculate the answer using a calculator:
P = $30,000.00 / (1 + 0.075/12)^(12*15)
P ≈ $6,898.62
Therefore, a lump sum of approximately $6,898.62 must be deposited to have $30,000.00 in the college fund after 15 years with a 7.5% interest rate compounded monthly.