On the day of a child's birth, a deposit of $30,000 is made in a trust fund that pays 3% interest, compounded continuously. Determine the balance in this account on the child's 30th birthday. (Round your answer to two decimal places.)
e^rt = e^(.03*30) = e^.9 = 2.4596
times 30,000 = $ 73,788.09
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At the birth of a baby, a couple decides to make an initial investment of C at the rate of 7% compounded annually so that the amount will grow to $30,000 by her 10th birthday. What should their initial investment be? Round to the nearest dollars.
On the day of a child's birth, a parent deposits $25,000 in a trust fund that pays 5% interest, compounded continuously. Determine the balance in this account on the child's 24th birthday. (Round your answer to two decimal places.)
Well, let me tell you, compound interest sure knows how to party! To find the balance, we can use the formula A = P * e^(rt), where A is the balance, P is the principal amount ($30,000 in this case), r is the interest rate (3% or 0.03), and t is the time in years (30 in this case). So, grab your party hats and let's do some math!
First, we need to convert the interest rate from a percentage to a decimal. 3% is equal to 0.03. Excellent! Now, let's plug these values into the formula:
A = 30000 * e^(0.03*30)
Now, let's channel our inner mathematician and calculate that big ol' number. Drumroll, please...
A ≈ 30,000 * 2.208039355
Let me grab my clown calculator for this one!
A ≈ 66,241.18
Ta-da! The balance in the account on the child's 30th birthday will be approximately $66,241.18. I hope that sum puts a smile on your face!
To determine the balance in the account on the child's 30th birthday, we need to use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period (in years)
In this case, the initial deposit (P) is $30,000 and the interest rate (r) is 3% (or 0.03 in decimal form). We need to find the balance after 30 years (t = 30).
Plugging in these values into the formula, we have:
A = $30,000 * e^(0.03 * 30)
To calculate this expression, we need to know the value of Euler's number, e, raised to the power of 0.03 multiplied by 30.