the graph shows the effect of inflation. the effect of inflation on investments $12,000 $10,000 $8,000…

the graph shows the effect of inflation. the effect of inflation on investments $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 initial investment 5 years 10 years 15 years 20 years 1% annual inflation 3% annual inflation approximately how much of the initial investment’s value would be lost after 15 years at 3% inflation? 15% 20% 40% 50%

the graph shows the effect of inflation. the effect of inflation on investments $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 initial investment 5 years 10 years 15 years 20 years 1% annual inflation 3% annual inflation approximately how much of the initial investment’s value would be lost after 15 years at 3% inflation? 15% 20% 40% 50%

Answer

Explanation:

Step1: Assume initial investment is $10000$.

Let the initial value $V_0 = 10000$.

Step2: Use compound - inflation formula for 15 years at 3% inflation.

The formula for the value $V$ after $n$ years with an annual inflation rate $r$ is $V=V_0(1 - r)^n$, where $r = 0.03$ and $n = 15$. So $V = 10000\times(1 - 0.03)^{15}=10000\times0.97^{15}$.

Step3: Calculate $0.97^{15}$.

$0.97^{15}\approx0.633$. So $V\approx10000\times0.633 = 6330$.

Step4: Calculate the percentage loss.

The loss amount is $10000 - 6330=3670$. The percentage loss $P=\frac{10000 - 6330}{10000}\times100%=\frac{3670}{10000}\times100% = 36.7%\approx40%$.

Answer:

C. 40%