Pete Air wants to buy a used Jeep in 5 years. He estimates the Jeep will cost $15,000. Assume Pete invests $10,000 now at 12% interest compounded semiannually.
Calculate the maturity value of the investment
A = P(1+ r/)^nt
A = 10000(1 + .12/2)^2(5)
= 10000(1.06)^10
= $ 17,908.48
Yes
Well, Pete Air is definitely trying to make some "Jeep" money! Let's calculate the maturity value of his investment.
First, we need to figure out how many semiannual periods there are in 5 years. Since there are two semiannual periods in a year, we multiply 5 by 2, which gives us 10.
Next, we plug the values into the compound interest formula:
Maturity Value = Principal Amount × (1 + (Interest Rate / Number of Periods))^(Number of Periods × Number of Years)
Maturity Value = $10,000 × (1 + (12% / 2))^(10 × 5)
Maturity Value = $10,000 × (1 + 0.06)^50
Maturity Value = $10,000 × (1.06)^50
Now, I'm going to need the help of my handy calculator to compute that exact value for you.
**Calculating**
*Beep boop beep*
**Calculating complete**
And the maturity value of Pete's investment comes out to be approximately $31,185.61.
So, Pete will have around $31,185.61 when he's ready to go "Jeepin'" in 5 years.
To calculate the maturity value of the investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Maturity value of the investment
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given values:
P = $10,000
r = 12% = 0.12 (as a decimal)
n = 2 (compounded semiannually)
t = 5 years
Substituting the values into the formula, we get:
A = $10,000(1 + 0.12/2)^(2 * 5)
A = $10,000(1 + 0.06)^10
A = $10,000(1.06)^10
Calculating this expression, we find:
A ≈ $10,000(1.790847)
A ≈ $17,908.47
Therefore, the maturity value of the investment after 5 years will be approximately $17,908.47.
To calculate the maturity value of the investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Maturity Value
P = Principal amount (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Pete invested $10,000 at an annual interest rate of 12% compounded semiannually for 5 years.
To calculate the maturity value, we need to first convert the annual interest rate to a semiannual interest rate. Since interest is compounded semiannually, the annual interest rate of 12% is divided by 2 to get a semiannual interest rate of 6%.
Now we can substitute the values into the formula:
A = $10,000 (1 + 0.06/2)^(2*5)
Simplifying further:
A = $10,000 (1 + 0.03)^10
Using a calculator, we can evaluate the calculation:
A = $10,000 (1.03)^10
A ≈ $10,000 * 1.34392
A ≈ $13,439.20
Therefore, the maturity value of the investment after 5 years would be approximately $13,439.20.
Principal, P = $10000
interest per period of 6 months, i = 0.06
number of periods, n = 5 yrs/0.5 yr = 10
Value at maturity
=P(1+i)^n
He will have money to pay for the Jeep, and perhaps the sales taxes as well.