A man deposit 24, 000 into a mutual fund that is expected to grow at a annual rate of 8%. What will be the rate of the investment be in 2 years
4 years
6 years
8 years
To calculate the future value of an investment over a period of time, we can use the formula:
Future Value = Present Value * (1 + Rate of Return)^Time
Given:
Present Value (P) = $24,000
Rate of Return (R) = 8% or 0.08
Calculating the future value after 2 years:
Future Value after 2 years = $24,000 * (1 + 0.08)^2
Future Value after 2 years = $24,000 * (1.08)^2
Future Value after 2 years = $24,000 * 1.1664
Future Value after 2 years = $27,993.60
Calculating the future value after 4 years:
Future Value after 4 years = $24,000 * (1 + 0.08)^4
Future Value after 4 years = $24,000 * (1.08)^4
Future Value after 4 years = $24,000 * 1.3605
Future Value after 4 years = $32,532
Calculating the future value after 6 years:
Future Value after 6 years = $24,000 * (1 + 0.08)^6
Future Value after 6 years = $24,000 * (1.08)^6
Future Value after 6 years = $24,000 * 1.5939
Future Value after 6 years = $38,254.40
Calculating the future value after 8 years:
Future Value after 8 years = $24,000 * (1 + 0.08)^8
Future Value after 8 years = $24,000 * (1.08)^8
Future Value after 8 years = $24,000 * 1.8061
Future Value after 8 years = $43,346.40
Therefore, the future value or rate of the investment after:
2 years = $27,993.60
4 years = $32,532
6 years = $38,254.40
8 years = $43,346.40
To find the growth rate of an investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount P is $24,000 and the annual interest rate r is 8% (or 0.08 in decimal form). Since the question does not mention how many times the interest is compounded per year (n), let's assume it is compounded annually (n = 1).
1. In 2 years:
We want to find the interest rate for the investment after 2 years. Plugging the given values into the compound interest formula:
A = $24,000 * (1 + 0.08/1)^(1*2)
A = $24,000 * 1.08^2
A ≈ $24,000 * 1.1664
A ≈ $27,993.60
To find the growth rate, we need to calculate the difference between the future value (A) and the principal amount (P), and divide it by the principal amount. Then multiply by 100 to convert it to a percentage:
Growth Rate = ((A - P) / P) * 100
Growth Rate = (($27,993.60 - $24,000) / $24,000) * 100
Growth Rate ≈ 16.64%
Therefore, the investment will have a growth rate of approximately 16.64% in 2 years.
2. In 4 years:
Using the same formula with t = 4 years:
A = $24,000 * (1 + 0.08/1)^(1*4)
A = $24,000 * 1.08^4
A ≈ $24,000 * 1.36049
A ≈ $32,571.76
Growth Rate = (($32,571.76 - $24,000) / $24,000) * 100
Growth Rate ≈ 35.71%
Therefore, the investment will have a growth rate of approximately 35.71% in 4 years.
3. In 6 years:
Again, using the same formula with t = 6 years:
A = $24,000 * (1 + 0.08/1)^(1*6)
A = $24,000 * 1.08^6
A ≈ $24,000 * 1.59781
A ≈ $38,347.44
Growth Rate = (($38,347.44 - $24,000) / $24,000) * 100
Growth Rate ≈ 59.78%
Therefore, the investment will have a growth rate of approximately 59.78% in 6 years.
4. In 8 years:
Lastly, using the formula with t = 8 years:
A = $24,000 * (1 + 0.08/1)^(1*8)
A = $24,000 * 1.08^8
A ≈ $24,000 * 2.158924
A ≈ $51,813.77
Growth Rate = (($51,813.77 - $24,000) / $24,000) * 100
Growth Rate ≈ 115.89%
Therefore, the investment will have a growth rate of approximately 115.89% in 8 years.