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Troyanec [42]
3 years ago
10

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 tak

e for the account value to reach 9600 dollars?
Mathematics
1 answer:
frozen [14]3 years ago
6 0

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.

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