# Find the future value in 15 years of a $20,000 payment today, if the interest rate is 3.8 % per...

## Question:

Find the future value in {eq}15 {/eq} years of a {eq}$ 20,000 {/eq} payment today, if the interest rate is {eq}3.8 \% {/eq} per year compounded continuously.

## Continuously Compounded Interest

The value of an investment or deposit into a savings account increases depending on the interest rate and how often that interest is added the account balance. For an initial investment of {eq}P {/eq} and an interest rate {eq}r {/eq}, the amount after {eq}t {/eq} years when this interest is compounded continuously can be found by calculating {eq}A = Pe^{rt} {/eq}.

## Answer and Explanation:

The future value of an investment or bank account is the value this amount grows to after time has passed. The initial value for this problem is $20,000, which was placed into an account with an interest rate of 3.8% per year. The value of this account after 15 years can be found as follows.

{eq}\begin{align*} A &= 20000e^{0.038(15)}\\ &= 20000e^{0.57}\\ &= 20000(1.76827)\\ &= 35365.4 \end{align*} {/eq}

Thus, the future value of this investment is $35,365.40.

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from High School Algebra I: Help and Review

Chapter 23 / Lesson 16