Randy invested his inheritance in an account that paid 6.1% interest, compounded continuously. After 5 years, he found that he now had $51, 426.94. What was the original amount of his inheritance?
amount(e^(.061)(5) = 51426.94
amount = 51426.94/e^(.061)(5)
= 37908.00
To find the original amount of Randy's inheritance, we can use the formula for continuous compound interest:
A = Pe^rt
Where:
A = Final amount after t years
P = Principal amount (original amount)
r = Annual interest rate (in decimal form)
t = Time in years
In this case, we have:
A = $51,426.94
r = 6.1% = 0.061 (since it's given as a percentage)
t = 5 years
Substituting these values into the formula, we get:
$51,426.94 = Pe^(0.061*5)
To solve for P, we can isolate it by dividing both sides of the equation by e^(0.061*5):
P = $51,426.94 / e^(0.061*5)
Using a calculator, we can evaluate e^(0.061*5) ≈ 1.338
P ≈ $51,426.94 / 1.338
P ≈ $38,365.96
Therefore, the original amount of Randy's inheritance was approximately $38,365.96.
To find the original amount of Randy's inheritance, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A is the final amount (given as $51,426.94),
P is the principal amount (original inheritance),
e is the base of the natural logarithm (approximately 2.71828),
r is the annual interest rate as a decimal (6.1% = 0.061),
t is the time in years (5 years).
Now we can solve for P:
51,426.94 = P * e^(0.061 * 5)
To isolate P, divide both sides of the equation by e^(0.061 * 5):
P = 51,426.94 / e^(0.061 * 5)
Using a calculator, we can evaluate the right side of the equation:
P ≈ 51,426.94 / 1.37068
P ≈ $37,580.87
Therefore, the original amount of Randy's inheritance was approximately $37,580.87.