Time to attain goal: Ryan Holmes wants to deposit $4,500 in a bank account that pays 8.25 percent annually. How many years will it take for his investment to grow to $10,000? (Round off to the nearest year.)
A) 8 years
B) 11 years
C) 10 years
D) 12 years

Question

Quizplus · Accepted Answer

We can solve for the number of years (t) using the formula for compound interest:

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

Where A is the future value, P is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we have:

10,000 = 4,500(1 + 0.0825/1)^(t*1)

Simplifying, we get:

2.2222 = (1.0825)^t

Taking the natural log of both sides, we have:

ln(2.2222) = t*ln(1.0825)

Solving for t, we get:

t = ln(2.2222)/ln(1.0825) ≈ 10.25 years

Rounding off to the nearest year, we get:

t ≈ 10 years

Therefore, the best choice is C, which gives the answer of 10 years.

Time to Attain Goal: Ryan Holmes Wants to Deposit $4,500