Question

Louise is planning to renovate her house. She intends to spend no more than $30 000. She has

$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.

Answer 1

Explanation:

To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money Louise will have after "t" years,

P is the initial investment of $20,000,

r is the annual interest rate of 4.28%,

n is the number of times the interest is compounded per year (12 times per year), and

t is the number of years.

We can rearrange this formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values:

t = (log(30000/20000)) / (log(1 + (0.0428/12)))

t = 5.97 years

Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.