Question

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.

Answer 1

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.