Manuel wants to purchase Subaru Impreza for $25,000 in 5 years
How much money should he invest in CD's today if the annual interest rate is 9%, compounded monthly? Show Work
Using the future value formula:
FV = PV * (1 + r/n)^(n*t)
where:
FV = future value (desired purchase price) = $25,000
PV = present value (amount to invest today) = ?
r = annual interest rate = 9%
n = number of times compounded per year = 12 (monthly)
t = time in years = 5
Substituting the values:
$25,000 = PV * (1 + 0.09/12)^(12*5)
Simplifying:
$25,000 = PV * 1.629
Dividing both sides by 1.629:
PV = $15,360.41
Therefore, Manuel should invest $15,360.41 in CD's today to have enough money to purchase the Subaru Impreza in 5 years, assuming an annual interest rate of 9% compounded monthly.
To determine how much money Manuel should invest in CD's today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment (in this case, $25,000)
P is the principal amount (the amount Manuel needs to invest today)
r is the annual interest rate (9% or 0.09)
n is the number of times the interest is compounded per year (monthly, so n = 12)
t is the number of years (5)
Substituting the given values into the formula, we have:
$25,000 = P(1 + 0.09/12)^(12*5)
To solve for P, we can rearrange the equation:
P = $25,000 / (1 + 0.09/12)^(12*5)
Calculating the exponential term first:
(1 + 0.09/12)^(12*5) = (1 + 0.0075)^60 ≈ 1.547
Now substituting the value:
P = $25,000 / 1.547
P ≈ $16,174.76
Therefore, Manuel should invest approximately $16,174.76 in CD's today to have $25,000 in 5 years with an annual interest rate of 9% compounded monthly.