Suppose you have $1 to put in an interest-bearing account for 1 year and are offered different options for interest rates and compounding frequencies (how often interest is calculated), as shown in the table. The highest interest rate is 100%, calculated once a year. The lower the interest rate, the more often it gets calculated. 1. Complete the table with expressions that represent the amount you will have after one year, and then evaluate each expression to find its value in dollars (round to 5 decimal places). value in dollars after 1 year frequency interest rate expression per year 1- (1+ 1)' |1 · (1+0.1)'0 1· (1+0.05)20 100% 1 10% |10 5% 20 1% 100 |0.5% 200 0.1% 1,000 0.01% |10,000 0.001% 100,000 2. Predict whether the account value will be greater than $3 if there is an option for a 0.0001% interest rate calculated 1 million times a year. Check your prediction. 3. What do you notice about the values of the account as the interest rate gets smaller and the frequency of compounding gets larger?

Suppose you have $1 to put in an interest-bearing account for 1 year and are offered different options for interest rates and compounding frequencies (how often interest is calculated), as shown in the table. The highest interest rate is 100%, calculated once a year. The lower the interest rate, the more often it gets calculated. 1. Complete the table with expressions that represent the amount you will have after one year, and then evaluate each expression to find its value in dollars (round to 5 decimal places). value in dollars after 1 year frequency interest rate expression per year 1- (1+ 1)' |1 · (1+0.1)'0 1· (1+0.05)20 100% 1 10% |10 5% 20 1% 100 |0.5% 200 0.1% 1,000 0.01% |10,000 0.001% 100,000 2. Predict whether the account value will be greater than $3 if there is an option for a 0.0001% interest rate calculated 1 million times a year. Check your prediction. 3. What do you notice about the values of the account as the interest rate gets smaller and the frequency of compounding gets larger?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

100%

Suppose you have $1 to put in an interest-bearing account for 1 year and are offered different options for interest rates and compounding frequencies (how often interest is calculated), as shown in the table. The highest interest rate is 100%, calculated once a year. The lower the interest rate, the more often it gets calculated.

1. Complete the table with expressions that represent the amount you will have after one year, and then evaluate each expression to find its value in dollars (round to 5 decimal places).

| interest rate | frequency per year | expression | value in dollars after 1 year |
|---------------|-------------------|------------------------------|-------------------------------|
| 100% | 1 | $ 1 \cdot (1 + 1)^1 $ | |
| 10% | 10 | $ 1 \cdot (1 + 0.1)^{10} $ | |
| 5% | 20 | $ 1 \cdot (1 + 0.05)^{20} $ | |
| 1% | 100 | | |
| 0.5% | 200 | | |
| 0.1% | 1,000 | | |
| 0.01% | 10,000 | | |
| 0.001% | 100,000 | | |

2. Predict whether the account value will be greater than $3 if there is an option for a 0.0001% interest rate calculated 1 million times a year. Check your prediction.

3. What do you notice about the values of the account as the interest rate gets smaller and the frequency of compounding gets larger?

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