Zinvests 10,000 every year starting from today for next 10 years. Suppose interest rate is 8% per annum compounded annually. Calculate future value of the annuity. Given that (1 +0.08)102.15892500.

To calculate the future value of an annuity where regular payments are made, the formula is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $FV$ is the future value of the annuity.
- $P$ is the annual payment (10,000 in this case).
- $r$ is the annual interest rate (8%, or 0.08).
- $n$ is the number of payments (10 years).

Given dataTo calculate the future value of an annuity where regular payments are made, the formula is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $FV$ is the future value of the annuity.
- $P$ is the annual payment (10,000 in this case).
- $r$ is the annual interest rate (8%, or 0.08).
- $n$ is the number of payments (10 years).

Given 
- $P = 10,000$
- $r = 0.08$
- $n = 10$
- $(1 + r)^{10} = 2.15892500$

Plugging in the values:

\[
FV = 10,000 \times \frac{2.15892500 - 1}{0.08}
\]

\[
FV = 10,000 \times \frac{1.15892500}{0.08}
\]

\[
FV = 10,000 \times 14.4865625
\]

\[
FV = 144,865.625
\]

So, the future value of the annuity is **$144,865.63** (rounded to two decimal places).

Would you like more details, or do you have any questions?

Here are five related questions to explore further:

1. How does changing the interest rate affect the future value of the annuity?
2. What would be the future value if Z invested $5,000 instead of $10,000 each year?
3. How would the calculation change if the interest were compounded semi-annually instead of annually?
4. What is the present value of the annuity using the same interest rate?
5. How does the number of years (n) impact the future value?

**Tip:** Always double-check the number of periods and the rate to ensure they align with the compounding frequency (e.g., annual, semi-annual).

Learn how to calculate the future value of an annuity with compound interest. Given an annual payment of $10,000 for 10 years at an 8% interest rate, find out the total future value using the annuity formula. Understand the impact of interest rates and payment periods on future savings.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation