Find the present value of the given amounts F with the indicated annual rate of return r, the number of years t, and the indicated compounding. (Round your answers to the nearest cent.)
F = $5600, r = 8.8%, t = 18
(a) compounded annually
$ 


(b) compounded quarterly
$ 


(c) compounded monthly
$ 


(d) compounded daily

remember using the finance tab of a ti84 calc



To find the present value (PV) of an amount $ F $ with a given annual interest rate $ r $, number of years $ t $, and different compounding periods, we use the following formula:

\[
PV = \frac{F}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ PV $ is the present value,
- $ F $ is the future value (in this case, \$5600),
- $ r $ is the annual interest rate (as a decimal, 0.088 for 8.8%),
- $ t $ is the number of years,
- $ n $ is the number of compounding periods per year (1 for annual, 4 for quarterly, 12 for monthly, and 365 for daily).

Let's compute each case using these values.

### (a) Compounded Annually (n = 1)
\[
PV = \frac{5600}{(1 + \frac{0.088}{1})^{1 \times 18}} = \frac{5600}{(1.088)^{18}}
\]

### (b) Compounded Quarterly (n = 4)
\[
PV = \frac{5600}{(1 + \frac{0.088}{4})^{4 \times 18}} = \frac{5600}{(1 + 0.022)^72} = \frac{5600}{(1.022)^{72}}
\]

### (c) Compounded Monthly (n = 12)
\[
PV = \frac{5600}{(1 + \frac{0.088}{12})^{12 \times 18}} = \frac{5600}{(1 + 0.0073333)^{216}} = \frac{5600}{(1.0073333)^{216}}
\]

### (d) Compounded Daily (n = 365)
\[
PV = \frac{5600}{(1 + \frac{0.088}{365})^{365 \times 18}} = \frac{5600}{(1 + 0.0002411)^{6570}} = \frac{5600}{(1.0002411)^{6570}}
\]

I'll calculate the values for each.Here are the present values for each compounding frequency:

- **(a) Compounded Annually**: \$1227.07
- **(b) Compounded Quarterly**: \$1168.76
- **(c) Compounded Monthly**: \$1155.52
- **(d) Compounded Daily**: \$1149.08

Would you like more details or have any further questions?

Here are 5 related questions you might explore:
1. What happens to the present value if the interest rate decreases to 5%?
2. How does doubling the number of years affect the present value?
3. What is the future value if we want to achieve a present value of \$2000 with these conditions?
4. How do continuous compounding formulas differ from periodic compounding?
5. What happens to the present value if we switch from daily to hourly compounding?

**Tip**: The more frequent the compounding, the smaller the present value for a given future amount.

Find the present value of the given amounts F with the indicated annual rate of return r, the number of years t, and the indicated compounding. (Round your answers to the nearest cent.) F = $5600, r = 8.8%, t = 18 (a) compounded annually (b) compounded quarterly (c) compounded monthly (d) compounded daily. Remember using the finance tab of a ti84 calc.

Learn how to calculate the present value of $5600 with an annual interest rate of 8.8% over 18 years for different compounding periods (annually, quarterly, monthly, and daily). This problem uses the compound interest formula, essential for students in higher math classes. Includes detailed solutions using a TI-84 calculator.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation