Final answer:
To find the time it takes for an investment to reach a specific amount with compound interest, one can rearrange the compound interest formula to solve for time. For the example provided, it takes approximately 14.4 years for $7,300 to grow to $8,560 at a 1.5% interest rate compounded quarterly, when calculated to the nearest tenth of a year.
Step-by-step explanation:
To calculate how long it would take for an investment of $7,300 to grow to $8,560 at an interest rate of 1.5% compounded quarterly, we use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case, we are solving for t, the time required. Therefore, we rearrange the formula to solve for t:
t = (log(A/P)) / (n*log(1 + r/n))
We insert the values into the equation:
t = (log(8560/7300)) / (4*log(1 + 0.015/4))
To the nearest tenth of a year, we calculate t using a calculator or logarithmic tables:
t ≈ (log(8560/7300)) / (4*log(1 + 0.015/4)) = 14.4 years (rounded to nearest tenth)
It will take approximately 14.4 years for the investment to grow from $7,300 to $8,560 with quarterly compounding at a 1.5% interest rate.