Question

Use logarithms to solve the problem. How long will it take $ 15,000 to grow to $ 18,000 if the investment earns interest at the rate of 5% year compounded monthly?

Answer 1

To find the time it will take for $15,000 to grow to $18,000 with a 5% interest rate compounded monthly, we can use logarithms. The calculation yields approximately 6.93 years.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

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

Where:

• A is the future amount, which in this case is $18,000
• P is the principal amount, which is $15,000
• r is the annual interest rate, which is 5%
• n is the number of times interest is compounded per year, which is 12 (monthly compounded)
• t is the time in years

We need to solve for t, so we can rearrange the formula:

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

Substituting the given values:

t = ln(18000/15000) / (12 * ln(1 + 0.05/12))

t ≈ 6.93 years