If you need $100,000 in 18 years, how much should you invest now if you can get 2.5%
compounded continuously?
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To solve this problem, we can use the formula for continuous compound interest:
A = P * e^(rt)
where:
A = the future amount
P = the principal (initial investment)
e = Euler's number (approximately 2.71828)
r = the interest rate
t = the time (in years)
We are given:
A = $100,000
r = 2.5% = 0.025
t = 18 years
Substituting the given values into the formula, we can solve for P:
$100,000 = P * e^(0.025 * 18)
Simplifying:
e^(0.025 * 18) = e^0.45 ≈ 1.5697
$100,000 = P * 1.5697
Dividing both sides of the equation by 1.5697:
P ≈ $63,670.06
So, you should invest approximately $63,670.06 now to have $100,000 in 18 years with continuously compounded interest at a rate of 2.5%.
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