Final answer:
To find the nominal rate of interest compounded quarterly, we can use the formula for compound interest. By substituting the given values into the formula and solving for the rate, we find that the nominal rate of interest compounded quarterly is approximately 7.62%.
Step-by-step explanation:
To find the nominal rate of interest compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the final amount (principal + interest)
- P is the principal amount
- r is the annual interest rate
- n is the number of times the interest is compounded in one year
- t is the number of years
In this case, we have:
- A = $13,000 + $8,407.27 = $21,407.27
- P = $13,000
- n = 4 (quarterly compounding)
- t = 6 years
Substituting these values into the formula, we have:
$21,407.27 = $13,000(1 + r/4)^(4*6)
Solving for r, we get:
1 + r/4 = (21,407.27/13,000)^(1/(4*6))
r/4 = [(21,407.27/13,000)^(1/(4*6))] - 1
r = 4 * {[(21,407.27/13,000)^(1/(4*6))] - 1}
Calculating this expression gives us r ≈ 0.0762, or 7.62%.