It takes 24 years for the account value to reach the $9600.
<u>Step-by-step explanation:</u>
<u>From the given data, it can be determined that :</u>
- Amount = $9600
- Principal = $3200
- Rate = 8.25% = 0.0825
Number of years should be calculated.
<u>To find the interest :</u>
Amount = Principal + Interest
Therefore, the interest can be calculated by the formula,
Interest = Amount - Principal
⇒ 9600 - 3200
⇒ 6400
The interest needed is 6400.
<u>To find the number of years required to reach this interest :</u>
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.
