If 2500 dollars is invested in an account for 10 years. Find the value of the investment at the end of 10 years if the interest is:

(a) 6.4% compounded annually: $ 

(b) 6.4% compounded semiannually: $ 

(a) 6.4% compounded quarterly: $ 

(b) 6.4% compounded monthly: $ 

(a) 6.4% compounded daily (ignore leap years): $ 


To calculate the value of the investment at the end of 10 years with different compounding periods, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the final amount of the investment,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the time in years.

For this problem:
- $ P = 2500 $,
- $ r = 6.4\% = 0.064 $,
- $ t = 10 $.

### (a) Compounded annually:
- $ n = 1 $.

### (b) Compounded semiannually:
- $ n = 2 $.

### (c) Compounded quarterly:
- $ n = 4 $.

### (d) Compounded monthly:
- $ n = 12 $.

### (e) Compounded daily:
- $ n = 365 $.

Let's calculate each of these values.Here are the values of the investment at the end of 10 years for different compounding periods:

(a) Compounded annually: \$4648.97

(b) Compounded semiannually: \$4693.90

(c) Compounded quarterly: \$4717.24

(d) Compounded monthly: \$4733.15

(e) Compounded daily: \$4740.94

Would you like more details or have any questions?

Here are five related questions you might want to explore:
1. How does continuous compounding differ from daily compounding?
2. What is the future value if the interest rate changes during the investment period?
3. How does the final amount change if the investment period is shorter, say 5 years?
4. What would the final amount be if you invested \$3000 instead of \$2500 at the same rate?
5. How would the investment grow if the rate was 5% instead of 6.4%?

**Tip**: The more frequent the compounding, the higher the final amount due to the interest-on-interest effect.

If 2500 dollars is invested in an account for 10 years. Find the value of the investment at the end of 10 years if the interest is: (a) 6.4% compounded annually, (b) 6.4% compounded semiannually, (c) 6.4% compounded quarterly, (d) 6.4% compounded monthly, (e) 6.4% compounded daily (ignore leap years).

Discover how to calculate the value of a $2500 investment over 10 years with an interest rate of 6.4%. Learn how the investment grows with annual, semiannual, quarterly, monthly, and daily compounding using the compound interest formula. Suitable for Grades 9-12.

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