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Investing $12,000 in a savings account at 2% annual interest compounded semiannually will result in approximately how much money after 5 years? Use the formula: A=P(1+(r)/(m))^(mt) $13,248.97 $13,255.

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Final answer:

Using the compound interest formula A=P(1+(r/m))^(mt), the future value of a $12,000 investment at 2% interest compounded semiannually after 5 years is approximately $13,255.47.

Step-by-step explanation:

Calculating Compound Interest on Savings

To calculate the future value of an investment with compound interest, the given formula is used:

A = P(1 + (r/m))^(mt)

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).

m is the number of times that interest is compounded per year.

t is the time the money is invested for in years.

For the given problem:

P = $12,000

r = 2% or 0.02

m = 2 (since the interest is compounded semiannually)

t = 5 years

Using the formula, we calculate the future value of the investment:

A = $12,000(1 + (0.02/2))^(2*5)

A = $12,000(1 + 0.01)^(10)

A = $12,000(1.01)^10

A = $12,000(1.104622125)

A = $13,255.47

This value is very close to the given option of $13,255, which suggests it is likely the correct amount assuming continuous compounding across full periods.

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