3200 dollars is placed in an account with an annual interest rate of 8.25%. To the nearest tenth of a year, how long will it take for the account value to reach 9600 dollars?

It takes 24 years for the account value to reach the $9600.

Step-by-step explanation:

From the given data, it can be determined that:

Amount = $9600 Principal = $3200 Rate = 8.25% = 0.0825

Number of years should be calculated.

To find the interest:

Amount = Principal + Interest

Therefore, the interest can be calculated by the formula,

Interest = Amount - Principal

⇒ 9600 - 3200

⇒ 6400

The interest needed is 6400.

To find the number of years required to reach this interest:

Use the formula for simple interest,

Simple interest = Pnr / 100

where,

P is the principal n is the number of years r is the rate

Substitute all the given values in the simple interest formula,

Simple interest = 3200 * n * 0.0825

6400 = 264 n

n = 6400 / 264

n = 24.2 which is approximately 24 years.

Therefore, it takes 24 years for the account value of 3200 dollars to reach 9600 dollars.