Final answer:
To find the nominal interest rate that Canary Company's investment earned over 5 years, we use the compound interest formula and rearrange it to solve for the interest rate. We then input the given values into the formula and calculate the nominal annual interest rate that compounded quarterly results in the investment growing from $101,400 to $126,600.
Step-by-step explanation:
The question involves calculating the nominal interest rate compounded quarterly for an investment that has grown from $101,400 to $126,600 over 5 years. To find the interest rate, we use the formula for compound interest:
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.
We rearrange the formula to solve for r:
r = n[(A/P)^(1/nt) - 1]
Inserting the values from the question:
A = $126,600, P = $101,400, n = 4 (quarterly), and t = 5 years.
Now we calculate:
r = 4[(126600/101400)^(1/(4*5)) - 1]
Once we calculate the value inside the brackets and subtract 1, we multiply the result by 4 to find the nominal interest rate. The calculated interest rate represents the nominal annual interest rate that the investment would have needed to grow to the given amount.