A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born to have $43,000 when the child reaches the age of 18? Assume the money earns 8% interest compounded quarterly. (Round your answer to two decimal places.)
will someone please help me? I need the answer
P(1 + .08/4)^(4*18) = 43000
P = 10333.70
To find the principal amount that needs to be deposited by the parents, we can use the future value formula:
Future Value = Principal * (1 + (interest rate / number of compounding periods))^(number of compounding periods * number of years)
In this case, the future value is $43,000, the interest rate is 8% (or 0.08), and the number of compounding periods is 4 (quarterly compounding). The number of years is 18.
So, the formula becomes:
$43,000 = Principal * (1 + (0.08 / 4))^(4 * 18)
To solve for the principal amount, we can rearrange the formula:
Principal = $43,000 / [(1 + (0.08 / 4))^(4 * 18)]
Now, let's calculate the principal using this formula and round the answer to two decimal places:
Principal = $43,000 / [(1 + 0.02)^(72)]
Principal = $43,000 / [1.02^(72)]
Principal = $43,000 / 3.8993727
Principal ≈ $11,030.67
Therefore, the principal amount that needs to be deposited by the parents when their child is born is approximately $11,030.67.