The nominal rate of interest is 8% and the rate of inflation is 5%. A single deposit is invested for 10 years. Let:
A= value of the investment at the end of 10 years measured in "constant dollars," i.e. in dollars valued at time 0.
B= value of the investment at the end of 10 years computed at the real rate of interest.
Find the ratio A/B.
To find the ratio A/B, we first need to calculate both values A and B separately.
Let's calculate A, the value of the investment at the end of 10 years measured in constant dollars.
The nominal rate of interest is 8%, which means the investment will grow by 8% each year. To calculate the future value of the investment after 10 years, we can use the compound interest formula:
A = P(1 + r)^n
Where:
A is the future value
P is the principal amount (initial investment)
r is the interest rate (in decimal form)
n is the number of compounding periods (in this case, 10 years)
Since we want the value in constant dollars, we need to adjust for inflation. The rate of inflation is 5%, which means the purchasing power decreases by 5% each year. We can adjust the future value using the following formula:
Adjusted A = A / (1 + inflation rate)^n
Now let's calculate B, the value of the investment at the end of 10 years computed at the real rate of interest.
The real rate of interest is the nominal rate minus the inflation rate. In this case, the inflation rate is 5% and the nominal rate is 8%, so the real rate would be 8% - 5% = 3%.
Using the compound interest formula, we can calculate B by adjusting for the real rate of interest:
B = P(1 + real interest rate)^n
Now that we have calculated A and B, we can find the ratio A/B:
Ratio A/B = A / B
Substitute the values you calculated for A and B into this equation to find the final answer.