Ernie invested $5,000 in an account for 3 years at 4% interest compounded quarterly Inflation over the period averaged 2% per year.
a. Calculate the value of the investment after 3 years
b. find the real rate of return on the investment and subsequently find the real value of the investment (inflation adjusted) after 3 years
a. To calculate the value of the investment after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Ernie invested $5,000, the annual interest rate is 4% (or 0.04 as a decimal), and interest is compounded quarterly (n = 4). He invested for 3 years. Plugging these values into the formula:
A = 5000 * (1 + 0.04/4)^(4*3)
A = 5000 * (1 + 0.01)^12
A = 5000 * 1.01^12
A ≈ $5,615.05
Therefore, the value of the investment after 3 years is approximately $5,615.05.
b. To find the real rate of return on the investment and subsequently find the real value of the investment after 3 years, we need to take into account the inflation rate.
The real rate of return is calculated as:
Real rate of return = (1 + nominal rate) / (1 + inflation rate) - 1
Given that the nominal rate is 4% (or 0.04 as a decimal) and the average inflation rate is 2% per year (or 0.02 as a decimal), we can substitute these values into the formula:
Real rate of return = (1 + 0.04) / (1 + 0.02) - 1
Real rate of return = 1.04 / 1.02 - 1
Real rate of return ≈ 0.0196 or 1.96%
So, the real rate of return on the investment is approximately 1.96%.
To find the real value of the investment after 3 years, we multiply the final amount (A) after 3 years by the factor (1 + real rate of return):
Real value = A * (1 + real rate of return)
Real value = $5,615.05 * (1 + 0.0196)
Real value ≈ $5,718.58
Therefore, the real value of the investment after 3 years (inflation adjusted) is approximately $5,718.58.
To calculate the value of the investment after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
a. Calculate the value of the investment after 3 years:
Given:
P = $5,000
r = 4% = 0.04 (as a decimal)
n = 4 (compounded quarterly)
t = 3 years
Using the formula:
A = 5000(1 + 0.04/4)^(4 * 3)
A = 5000(1 + 0.01)^(12)
A ≈ 5000(1.01)^(12)
A ≈ $5,615.13
Therefore, the value of the investment after 3 years is approximately $5,615.13.
b. To find the real rate of return on the investment and subsequently find the real value of the investment after 3 years (inflation adjusted), we need to account for inflation.
The real rate of return is the nominal rate of return minus the inflation rate. The nominal rate of return is the interest rate given (4%), and the inflation rate is given as 2% per year. Therefore, the real rate of return is:
Real rate of return = nominal rate of return - inflation rate
Real rate of return = 4% - 2%
Real rate of return = 2%
The real value of the investment after 3 years can be found by adjusting for inflation. We can use the formula:
Real value = Nominal value / (1 + inflation rate)^t
Given:
Nominal value = $5,615.13
Inflation rate = 2%
t = 3 years
Using the formula:
Real value = 5615.13 / (1 + 0.02)^3
Real value = 5615.13 / 1.061208
Real value ≈ $5,294.96
Therefore, the real value (inflation adjusted) of the investment after 3 years is approximately $5,294.96.
3 years is 12 quarters
a. 5000 [1 + (.04 / 4)]^12 = ?
b. real rate of return is ... {[1 + (.04 / 4)]^4 - 1 - .02} * 100% ... annually
real value is ... 5000 [1 + (real rate of return)]^3