You deposit $2000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 30 years?
You deposit $2000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 30 years?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Problem Statement:**
You deposit $2000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 30 years?
**Solution:**
The future value of the account is calculated to be $244,691.74.
**Explanation:**
To determine the future value of a series of annual deposits with compound interest, the formula for the future value of an annuity can be used:
\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]
Where:
- \(FV\) is the future value of the investment.
- \(P\) is the annual deposit ($2000).
- \(r\) is the annual interest rate (8% or 0.08).
- \(n\) is the number of years the money is invested (30).
Plug in the values:
\[
FV = 2000 \times \frac{{(1 + 0.08)^{30} - 1}}{0.08}
\]
This calculation results in approximately $244,691.74 after 30 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F282a3a3f-59f1-4615-b9ef-ee283c9e8b4d%2Fcdf5d8f4-f21c-4c84-8f43-ae8a83090672%2F1tdy3mu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
You deposit $2000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 30 years?
**Solution:**
The future value of the account is calculated to be $244,691.74.
**Explanation:**
To determine the future value of a series of annual deposits with compound interest, the formula for the future value of an annuity can be used:
\[
FV = P \times \frac{{(1 + r)^n - 1}}{r}
\]
Where:
- \(FV\) is the future value of the investment.
- \(P\) is the annual deposit ($2000).
- \(r\) is the annual interest rate (8% or 0.08).
- \(n\) is the number of years the money is invested (30).
Plug in the values:
\[
FV = 2000 \times \frac{{(1 + 0.08)^{30} - 1}}{0.08}
\]
This calculation results in approximately $244,691.74 after 30 years.
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