On the day a child was born, a lump sum P was deposited in a trust fund paying 6.5% interest compounded continuously. Use the balance A of the fund on the child's 29th birthday to find P. (Round your answer to the nearest cent.)
A = $5,000,000
P = $1
To find the initial deposit P, we can use the formula for continuous compound interest:
A = P * e^(rt),
where A is the final balance, P is the initial deposit, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time period.
In this case, we know that the final balance A is $5,000,000, the interest rate r is 6.5% (or 0.065 in decimal form), and the time period t is 29 years.
Plugging in these values, we get:
$5,000,000 = P * e^(0.065 * 29).
To isolate P, we need to divide both sides of the equation by e^(0.065 * 29):
P = $5,000,000 / e^(0.065 * 29).
Using a scientific calculator or online calculator, we can evaluate e^(0.065 * 29) to get the value of the exponential term. Then, perform the division to find the value of P.
After rounding to the nearest cent, we find that P is approximately $994.89.
5*10^6 = P*e^(29*0.065)
15.4249485 = lnP + 1.885000
lnP = 13.5399485
= $759,145.30