Write a compound interest function to model the following situation. Then, find the balance after the given number of years. $16,000 invested at a rate of 1.2% compounded monthly;7 years

A. A=16,100 (1.001)^7t; $17,469

B. A=16,100 (1.1)^12t; $6,766,377,209

C. A=16,100(1.001)^12t; $17,510

D. A=16,000(0.001)^12t; $24,150

Answer:

The answer to this question is:

A = 16,100(1.001)12t; $17,510

Step-by-step explanation:

The model function for compound interest is: [tex](16000[1.001]^{12t})[/tex]

The balance after 7 years will be $17409.

Let, P = the principle amount

r = the rate of interest, compounded monthly

t = the time period

Therefore, the amount will be

[tex]= P(1 + \frac{r}{1200})^{12t}[/tex]

Given, the invested amount is $16000.

The rate of interest is 1.2%, compounded monthly.

Total duration of investment is 7 years.

Therefore, the model function of this compound interest is:

= [tex]= (16000[1 + \frac{1.2}{1200}]^{12t})\\= (16000[1 +0.001]^{12t})\\= (16000[1.001]^{12t})\\[/tex]

The amount will be

[tex]= (16000[1.001]^{12t})\\= (16000[1.001]^{84})\\= 17409[/tex]

Therefore, after 7 years, the amount will be $17409.

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