Answer:
it will take at least 9 years for Lucy's investment to grow to more than $5,000. Since we can't have a fraction of a year, the answer is 10 years (rounded up from 9.09).
Explanation:
We can solve this problem by using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the initial investment (principal), which is $4,000 in this case
r = the interest rate per year, which is 3% expressed as a decimal (0.03)
n = the number of times the interest is compounded per year (we'll assume it's compounded annually, so n = 1)
t = the number of years
We want to find the number of years t it will take for the account balance to exceed $5,000. So we can set up the following inequality:
A > 5000
Substituting the values we have into the compound interest formula and simplifying, we get:
4000(1 + 0.03/1)^(1t) > 5000
Simplifying further, we get:
1.03^t > 1.25
To solve for t, we can take the logarithm of both sides of the inequality:
log(1.03^t) > log(1.25)
t*log(1.03) > log(1.25)
t > log(1.25) / log(1.03)
Using a calculator, we find that:
t > 9.09