Question

The equation log 1.134755 = log 1.003958333312t models the amount of time it takes a $10,000 investment to grow to $11,347.55 in a savings account where the annual interest is compounded monthly. solve for the amount of time

a. 32 months
b. 3 months
c. 27 months
d. 2 months

Answer 1

The time it takes for a $10,000 investment to grow to $11,347.55 with monthly compounded interest is found by solving the provided logarithmic equation, which comes out to be approximately 27 months, corresponding to option c.

The equation provided models the growth of a $10,000 investment over time with compound interest when the amount reaches $11,347.55. To find the number of months it takes for this investment growth, we rewrite the equation as:

1. log(1.134755) = log(1.003958333312t)
2. We observe that the logs on both sides can be dropped since log(a) = log(b) implies a = b.
3. 1.134755 = 1.003958333312t
4. We then use logarithms to solve for t.
5. t = log(1.134755) / log(1.003958333312)
6. By computing the right side using a calculator, we find that t ≈ 27.

This corresponds to option c, 27 months.