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What will $1000 be worth in 8 years if the nominal interest rate is 15% and (a) Interest is compounded every 4 months? (b) Interest is compounded every 4 years?

User Concept
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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

User Jrutter
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