Final answer:
If the nominal interest rate is 15%, the future value of $1000 compounded every 4 months would be approximately $5,320.99 after 8 years. If the interest is compounded every 4 years, the future value would be approximately $1,964.68.
Step-by-step explanation:
If the nominal interest rate is 15% and the interest is compounded every 4 months, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal (initial investment)
r = the nominal interest rate (expressed as a decimal)
n = the number of times interest is compounded per year (4 in this case)
t = the number of years
Substituting the given values into the formula:
A = 1000(1 + 0.15/4)^(4*8)
Solving this equation yields:
A ≈ $5,320.99
If the interest is compounded every 4 years, you can use the same formula but adjust the value of n to reflect the new compounding period. In this case, n would be 1/4 since the interest is compounded every 4 years:
A = 1000(1 + 0.15/1)^((1/4)*8)
Solving this equation yields:
A ≈ $1,964.68