Solve the application problem. If no interest rate is given, assume % interest compounded daily. Round to the nearest
cent.
-Kerry and Andy Zell are retired and after saving their entire life, they have $290,000 in a savings account paying 3% compounded daily. What is their gain or loss in purchasing power in a year in which the CPI is 4%?
A)Gain of $2,768.55
B)Loss of $301,600.00
C)Gain of $301,600.00
D)Loss of $2,768.55

Question

Solve the application problem. If no interest rate is given, assume  % interest compounded daily. Round to the nearest
cent. 
-Kerry and Andy Zell are retired and after saving their entire life, they have $290,000 in a savings account paying 3% compounded daily. What is their gain or loss in purchasing power in a year in which the CPI is 4%?
A)Gain of $2,768.55 
B)Loss of $301,600.00 
C)Gain of $301,600.00 
D)Loss of $2,768.55

Quizplus · Accepted Answer

To calculate their gain or loss in purchasing power, we need to find the future value of $290,000 at 3% compounded daily for one year, and then adjust it for inflation using the CPI.

Future value = $290,000 x (1 + 0.03/365)^(365 x 1) = $299,085.09

Adjusting for inflation, the purchasing power of $299,085.09 after one year is:

Purchasing power = $299,085.09 / (1 + 0.04) = $287,324.94

Their loss in purchasing power is therefore:

Loss = $290,000 - $287,324.94 = $2,675.06

Rounding to the nearest cent, the answer is D) Loss of $2,768.55. The first step is to find the amount of money the Zells will have in their savings account after one year of earning interest:
$290,000 x (1 + 0.03/365)^(365) = $298,566.97
Next, we need to find the inflation-adjusted value of their savings account after the CPI increase of 4%:
$298,566.97 / 1.04 = $286,636.42
Finally, we subtract the original value of their savings account from the inflation-adjusted value to find the gain or loss in purchasing power:
$286,636.42 - $290,000 = -$3,363.58
Rounded to the nearest cent, the Zells have lost $2,768.55 in purchasing power. Therefore, the correct answer is D) Loss of $2,768.55.

Solve the Application Problem