Suppose $2,000.00 dollars is invested in an account for 13 years. Find the value of the investment at the end of 13 years if the interest is:
(a) 5.2% compounded annually:
(b) 5.2% compounded semiannually:
(c) 5.2% compounded quarterly:
(d) 5.2% compounded monthly:
(e) 5.2% compounded daily (ignore leap years): and answers

To calculate the future value of an investment with compound interest, we use the compound interest formula:

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

Where:
- $ A $ is the future value of the investment
- $ P $ is the principal amount (initial investment)
- $ r $ is the annual interest rate (in decimal form)
- $ n $ is the number of times the interest is compounded per year
- $ t $ is the time the money is invested for, in years

The principal amount ($ P $) is $2,000.00, the interest rate ($ r $) is 5.2% or 0.052 in decimal, and the time ($ t $) is 13 years.

### (a) Compounded annually:
For annual compounding, $ n = 1 $.

\[
A = 2000 \left(1 + \frac{0.052}{1}\right)^{1 \times 13}
\]

### (b) Compounded semiannually:
For semiannual compounding, $ n = 2 $.

\[
A = 2000 \left(1 + \frac{0.052}{2}\right)^{2 \times 13}
\]

### (c) Compounded quarterly:
For quarterly compounding, $ n = 4 $.

\[
A = 2000 \left(1 + \frac{0.052}{4}\right)^{4 \times 13}
\]

### (d) Compounded monthly:
For monthly compounding, $ n = 12 $.

\[
A = 2000 \left(1 + \frac{0.052}{12}\right)^{12 \times 13}
\]

### (e) Compounded daily (assuming 365 days in a year):
For daily compounding, $ n = 365 $.

\[
A = 2000 \left(1 + \frac{0.052}{365}\right)^{365 \times 13}
\]

I'll calculate the values now.

Suppose $2,000.00 dollars is invested in an account for 13 years. Find the value of the investment at the end of 13 years if the interest is: (a) 5.2% compounded annually, (b) 5.2% compounded semiannually, (c) 5.2% compounded quarterly, (d) 5.2% compounded monthly, (e) 5.2% compounded daily (ignore leap years).

Learn how to calculate the future value of an investment of $2,000 over 13 years with a 5.2% interest rate compounded annually, semiannually, quarterly, monthly, and daily. This problem covers the compound interest formula and is suitable for high school students (Grades 9-12).

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