Ask Me Help Desk - Exponential and Logarithmic Equations

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Exponential and Logarithmic Equations

Complete the table for a savings account subject n compoundings yearly
[A=P(1+r/n) with an exponent nt]

amount invested is 12,500 number of compounding periods is 4 annual interest rate is 5.75% and accumulated amount is 20,000

I do not understand how to get the time t in years

Susan

Just plug in all of the other parameters and solve for t.

$20000=12500(1+\frac{.0575}{4})^{4t}$

Now, we solve for t. From here on out I am going to use fractions instead of decimals.

$1+(.0575/4)=\frac{1623}{1600}$ .

$20000=12500(\frac{1623}{1600})^{4t}$

$\frac{8}{5}=(\frac{1623}{1600})^{4t}$

$ln(\frac{8}{5})=4t\cdot\ln(\frac{1623}{1600})$

Now, finish? Solve for t.

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