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8 June, 09:18

tina invests in $1,200 in a account with an interest rate of 6.25%. How many years for the account to reach $11,900.

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  1. 8 June, 10:47
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    Hello!

    To find the amount of years it will take for Tina's account to reach $11,900, we need to first, write an equation, then we would solve for the amount of years it would take using logarithms.

    1. Write an equation

    Since this question is a compound interest problem, we would write the equation in a format like this: y = a (1 + n) ^x.

    In this equation, y is the final value, a is the beginning value, n is the interest rate, and x is the amount of years. Since we are given the values of y, a, and n, we can substitute those values into the equation.

    11900 = 1200 (1 +.0625) ^x

    Notice that 6.25% was converted to 0.0625. To convert percentages to a decimal, divide the percent by 100.

    2. Solve for x using logarithms

    11900 = 1200 (1.0625) ^x (divide by 1200 to both sides)

    11900/1200 = 1.0625^x (take the log of both sides)

    log 11900/1200 = x log 1.0625 (divide both sides by log 1.0625)

    log 11900/1200 / log 1.0625 = x

    x = 37.8429 ...

    This can be rounded to about 37.84 years.

    Therefore, it will take about 37.84 years for Tina's account to reach 11,900 dollars.
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