Question

Suzy invests $600 in an account that pays 1.5% interest BIANNUALLY. How long will it take for her account balance to reach $10,000?

Answer 1

`color(blue)(t ~~ 188.277)`
It would take about 188.277 years for her account balance to reach $10,000.

Explanation:

Since this is a compounding interest equation, we will use this formula:
`A = P(1 + r/n)^(n*t)`
A = End Amount
P = Initial Amount
r = rate
n = times compounded per `t`
t = amount of years

Fill in the variable from the word problem:
`10000 = 600(1 + 0.015/2)^(2*t)`

Finally, solve for t:
1) Divide both sides by 600
`16.67 = (1.0075)^(2t)`
2) Using logarithms, rewrite the equation to undo the exponential variable:
`log_1.0075(16.67) = 2t`
3) Using the Logarithm Base Change rule, we can make the logarithm more "calculator friendly":
`log(16.67)/log(1.0075) = 2t`
4) Plug into a calculator(I recommend this one) and solve for t:
`t ~~ 188.277`