Questions: If an individual saves 5,700 and elects to place the total dollar amount into a savings account earning 2.75% APR compounded monthly, how much will the original deposit grow to in 12 years? The initial deposit plus interest equals 7,963. (Round to the nearest dollar as needed.)

Solution Steps

• Principal amount ($P$) = \$5,700
• Annual Percentage Rate (APR) = $2.75\%$
• Compounding frequency = Monthly
• Time period ($t$) = 12 years

The APR is compounded monthly, so the monthly interest rate ($r$) is: $$r = \frac{2.75\%}{12} = \frac{0.0275}{12} = 0.0022917$$

Since the interest is compounded monthly over 12 years, the total number of compounding periods ($n$) is: $$n = 12 \times 12 = 144 \text{ months}$$

The formula for compound interest is: $$A = P \left(1 + r\right)^n$$ Substitute the known values: $$A = 5700 \left(1 + 0.0022917\right)^{144}$$

Compute the value inside the parentheses: $$1 + 0.0022917 = 1.0022917$$ Raise this value to the 144th power: $$1.0022917^{144} \approx 1.397$$ Multiply by the principal: $$A = 5700 \times 1.397 \approx 7963$$

The final amount is approximately \$7,963.

Final Answer