The amount of money that needs to be deposited into an account to reach some future goal is called the present value. The following table gives the present value (to the nearest dollar) for an account that earns 10% compounded annually so that the account value will be $50,000 after intervals ranging from 1 to 7 years. Years Present value 1 $45,455 2 41,322 3 37,566 4 34,151 5 31,046 6 28,224 7 26,658 (a) Using x as the years and y as the present value (in dollars), develop an exponential model for these data. (Round your numerical values to four decimal places.) y = (b) Use the model to find the present value (to the nearest dollar) of this account for its value to be $50,000 after 12 years.
The amount of money that needs to be deposited into an account to reach some future goal is called the present value. The following table gives the present value (to the nearest dollar) for an account that earns 10% compounded annually so that the account value will be $50,000 after intervals ranging from 1 to 7 years. Years Present value 1 $45,455 2 41,322 3 37,566 4 34,151 5 31,046 6 28,224 7 26,658 (a) Using x as the years and y as the present value (in dollars), develop an exponential model for these data. (Round your numerical values to four decimal places.) y = (b) Use the model to find the present value (to the nearest dollar) of this account for its value to be $50,000 after 12 years.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 68SE: An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000...
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The amount of money that needs to be deposited into an account to reach some future goal is called the present value. The following table gives the present value (to the nearest dollar) for an account that earns 10% compounded annually so that the account value will be $50,000 after intervals ranging from 1 to 7 years.
| Years | Present value |
|---|---|
| 1 | $45,455 |
| 2 | 41,322 |
| 3 | 37,566 |
| 4 | 34,151 |
| 5 | 31,046 |
| 6 | 28,224 |
| 7 | 26,658 |
(a)
Using x as the years and y as the present value (in dollars), develop an exponential model for these data. (Round your numerical values to four decimal places.)
y =
(b)
Use the model to find the present value (to the nearest dollar) of this account for its value to be $50,000 after 12 years.
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