An investor places $100,000 in a bond that earns 10% interest per year for 5 years. During this period, inflation averages 10% per year. At the end of 5 years, the nominal value of the investment (the value before accounting for inflation) grows to $161,051 Use the following formulas to calculate the real value of the investment in today's dollars. Inflation factor formula: inflation factor is equal to open paren 1 plus annual inflation rate close paren to the number of years th power Present value formula: present value=(future nominal value)/(inflation factor) How did inflation affect the investment's real value and nominal value after 5 years?
Answer
A
The nominal value increased significantly, but the real value declined to 80 dollars comma 000 due to inflation.
B
The real value of the investment remained the same, while the nominal value stayed at 100 dollars comma 000.
C
The nominal value increased to 161 dollars comma 051, and the real value grew faster than inflation.
D
The nominal value increased to 161 dollars comma 051, but the real value remained constant at 100 dollars comma 000 due to inflation.
Explanation
The five-year inflation factor is (1 + 0.10)^5 = 1.61051. Dividing the future nominal value, $161,051, by 1.61051 gives a real value of $100,000 in today’s dollars. Thus, the nominal value increased to $161,051, while the real value remained constant at $100,000, as choice D states.
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