Rico can invest money at 10%/a compounded quarterly. He would like
$15 000 in 10 years. How much does he need to invest now?
You are wrong
The balance gets multiplied bu 1.025 forty times.
X*(1.025)^40 = 15,000.
2.685063838X = 15,000.
X = $ 5586.46
To find out how much Rico needs to invest now to reach $15,000 in 10 years at an interest rate of 10% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (in this case, $15,000)
P = the principal amount (the initial investment we're trying to find)
r = the annual interest rate (10% or 0.10)
n = the number of times interest is compounded per year (4, because it's compounded quarterly)
t = the number of years (10)
We need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Now we can plug in the values:
P = 15000 / (1 + 0.10/4)^(4*10)
First, simplify the expression inside the parentheses:
P = 15000 / (1.025)^(40)
Next, calculate the exponent:
P = 15000 / (1.025^40)
Using a calculator or a spreadsheet, we find that 1.025^40 is approximately equal to 1.48861.
P = 15000 / 1.48861
Finally, divide $15,000 by 1.48861 to find the initial investment:
P ≈ $10,081.68
Therefore, Rico needs to invest approximately $10,081.68 now.
PV = A( 1+i)^n
=15,000(1+0.025)^-40
=$5586.46