Question

Nicole deposited $5000 into an account with a 2.4% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $6500? Do not round any intermediate computations, and round your answer to the nearest hundredth. If necessary, refer to the list of financial formulas. years X - ?​

Answer 1

10.94 years

Explanation:

We're gonna use the compound interest formula: P = A(1 + r/n)ⁿˣ

P = Final amount (6500)

A = Starting amouint (5000)

r = rate (0.024)

n = number of times applied (12)

x = number of years

6500 = 5000(1 + 0.024/12)¹²ˣ

First, divide both sides by 5000

(1 + 0.024/12)¹²ˣ = 6500/5000 = 1.3

Then solve the equation inside the parenthesis

1.002¹²ˣ = 1.3

Take log₁.₀₀₂ from both sides

12x = log₁.₀₀₂(1.3)

12x = 131.3133

Finally divide both sides by 12

12x/12 = 131.3133/12

x = 10.942775