miranda has put aside $5,000 in a savings account earning a nominal interest rate of 6%. over the first…

miranda has put aside $5,000 in a savings account earning a nominal interest rate of 6%. over the first year, she earns $300 in interest. however, the rate of inflation is 3%. what is the actual purchasing power of mirandas savings?\n\n$4,850\n$5,000\n$5,150\n$5,300

miranda has put aside $5,000 in a savings account earning a nominal interest rate of 6%. over the first year, she earns $300 in interest. however, the rate of inflation is 3%. what is the actual purchasing power of mirandas savings?\n\n$4,850\n$5,000\n$5,150\n$5,300

Answer

Explanation:

Step1: Calculate the real interest rate

$$r = i - \pi = 6% - 3% = 3%$$

Step2: Calculate the nominal value after one year

$$FV = P \times (1 + i) = $5,000 \times (1 + 0.06) = $5,300$$

Step3: Adjust for inflation to find purchasing power

$$PP = \frac{FV}{1 + \pi} = \frac{$5,300}{1 + 0.03}$$

Step4: Perform the final division

$$PP = \frac{$5,300}{1.03} \approx $5,145.63$$

Step5: Use the real interest rate approximation

$$PP \approx P \times (1 + r) = $5,000 \times (1 + 0.03) = $5,150$$

Answer:

$5,150