Question

Curtis wants to save money for a trip overseas. Curtis invests $800 in an account that pays an interest rate of 6.25%.

How many years will it take for the account to reach $10,800? Round your answer to the nearest hundredth.

Answer 1

Explanation:

We can use the formula for compound interest to solve this problem:

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

Where:

- A is the final amount

- P is the initial deposit

- r is the annual interest rate as a decimal

- n is the number of times the interest is compounded per year

- t is the number of years

In this case, we want to find t, so we can rearrange the formula:

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

Plugging in the values we know:

P = 800

r = 0.0625

A = 10,800

n = 1 (interest is compounded annually)

t = log(10800/800) / (1 * log(1 + 0.0625/1)) = 19.57

So it will take approximately 19.57 years for Curtis' account to reach $10,800. Rounded to the nearest hundredth, the answer is 19.57 years.