Compounded Interest Continuously

Question

How much would you need to deposit in an account now in order to have $6,000 in 15 years? Assume the account earns 3% interest compounded continuously.

Answer 1

the underlying formula that you want to use here for continuous compounding interest is

A = P*e^(rt)

for this scenario that means taking

6000 = P*e^(0.03*15)

P = 6000 / e^(0.45)

P = 3825.77

meaning that the required deposit in this scenario is $3,825.77

Answer 2

You would use the formula FV = PV * e^(Yr), where FV is future value, PV is present value, e is a constant which equals about 2.71828, Y is the number of years, and r is the rate. I have included a link with an explanation for the calculus behind how that formula is derived if you are interested http://www.moneychimp.com/articles/finworks/continuous_compounding.htm.

Using that formula, $6,000 = PV * e^(15x.03). Doing the algebra, you come to a value of $3,825.77.