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Problem 10

# Determine the simple interest rate at which $$\ 1200$$ will grow to $$\ 1250$$ in 8 mo.

Expert verified
The simple interest rate at which $$\1200$$ will grow to $$\1250$$ in 8 months is approximately $$6.25\%$$.
See the step by step solution

## Step 1: Calculate the Interest Amount

Since we know the principal amount (P) and the final amount, we can calculate the interest amount (I) by subtracting the principal amount from the final amount: $$I = \ 1250 - \ 1200$$ $$I = \ 50$$ The interest amount (I) is $$\50$$.

## Step 2: Substitute the Known Values and Solve for R

Now, we can substitute the known values (P, I, and T) in the simple interest formula: $$\50 = \1200 × R × \frac{8}{12}$$ Here the time (T) is given in months, we must convert it to years by dividing by 12. Therefore, T becomes $$\frac{8}{12}$$. After substituting the remaining values, divide both sides by $$1200$$ and the fraction $$\frac{8}{12}$$: $$R = \frac{\50}{\1200 × \frac{8}{12}}$$

## Step 3: Convert the Decimal Value to a Percentage

Solve the expression on the right-hand side to find R: $$R ≈ 0.0625$$ To convert the decimal value of R to a percentage, multiply by 100: Simple Interest Rate $$≈ 0.0625 × 100 = 6.25\%$$ Thus, the simple interest rate at which $$\1200$$ will grow to $$\1250$$ in 8 months is approximately $$6.25\%$$.

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