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Suppose you have [tex]$2550 in your savings account at the end of a certain period of time. You invested $[/tex]1900 at a 2.67% simple annual interest rate. How long, in years, was your money invested? State your result to the nearest hundredth of a year.



Answer :

GinnyAnswer
To determine the number of years your money was invested, we can use the formula for simple interest. The formula for the amount [tex]\( A \)[/tex] in a simple interest scenario is given by:

[tex]\[ A = P(1 + rt) \][/tex]

where:
- [tex]\( A \)[/tex] is the final amount,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate,
- [tex]\( t \)[/tex] is the time in years.

We need to rearrange this formula to solve for [tex]\( t \)[/tex]:

[tex]\[ t = \frac{A}{P} - 1 \div r \][/tex]

Given the values:
- Principal amount [tex]\( P \)[/tex] = [tex]$1900, - Final amount \( A \) = $[/tex]2550,
- Annual interest rate [tex]\( r \)[/tex] = 2.67% (which is equal to 0.0267 when converted to a decimal).

We follow these steps:

1. Compute [tex]\( \frac{A}{P} \)[/tex]:
[tex]\[ \frac{2550}{1900} = 1.3421052631578947 \][/tex]

2. Subtract 1:
[tex]\[ 1.3421052631578947 - 1 = 0.3421052631578947 \][/tex]

3. Divide by the annual interest rate [tex]\( r \)[/tex]:
[tex]\[ \frac{0.3421052631578947}{0.0267} = 12.812931204415532 \][/tex]

So, the time [tex]\( t \)[/tex] in years is approximately 12.81 when rounded to the nearest hundredth.

Hence, your money was invested for approximately 12.81 years.

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