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Problem 1269

If $$\ 100$$ is invested at $$3 \%$$ interest compounded annually, how much will it amount to at the end of 18 yrs.?

Expert verified
After investing $$\100$$ at a $$3\%$$ annual interest rate compounded annually for 18 years, the final amount will be approximately $$\170.80$$.
See the step by step solution

Step 1: Convert the annual interest rate to a decimal

To convert the annual interest rate of 3% to a decimal, we will divide it by 100: $$r = \frac{3}{100} = 0.03$$

Step 2: Substitute the given values into the compound interest formula

Now, we will substitute the given values into the compound interest formula: $$A = P(1 + r/n)^{nt}$$ $$A = 100(1 + 0.03/1)^{1 \cdot 18}$$

Step 3: Simplify the expression

Let's simplify the expression: $$A = 100(1 + 0.03)^{18}$$ $$A = 100(1.03)^{18}$$

Step 4: Calculate the final amount

Now, we will calculate the final amount by raising 1.03 to the power of 18 and multiplying the result by 100: $$A = 100 \cdot 1.03^{18} \approx 170.80$$ So, after 18 years, the initial investment of $$100 will amount to approximately$$170.80.

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