Explanation:
Based on the information given, this is a compound interest problem.
We can use the formula: A = P(1 + r/n)^(nt) where:
A = the final amount
P = the principal (or initial amount deposited) r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this problem, we want to find the principal (P) that must be deposited in order to have $38,000 when the child reaches 18. We know that the interest rate is 4%, compounded monthly (so n = 12). The time is 18 years.
Plugging in the values, we get: $38,000 = P(1 + 0.04/12)^(12*18)
Simplifying the exponent, we get: $38,000 = P(1 + 0.003333)^216 $38,000 = P(1.003333)^216
Dividing both sides by (1.003333)^216, we get: P = $38,000 / (1.003333)^216 P = $17,714.54
(rounded to two decimal places) Therefore, the parents must deposit $17,714.54 when their child is born in order to have $38,000 when the child reaches 18, assuming the money earns 4% interest compounded monthly.