Patrick invests a sum of money for 2.5 years at 12% p.a. compounded monthly. If he earns $11305 after 2.5 years, how much is his investment?
let the investment be P
P(1.01)^30 = 11305
P = 11305/1.01^30 = 8387.44
50000
32500
To find out the initial investment made by Patrick, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (which is $11305),
P is the principal amount (the initial investment),
r is the annual interest rate (12%),
n is the number of times interest is compounded per year (12, for monthly compounding),
t is the time in years (2.5 years).
Using the given information, we can plug it into the formula:
$11305 = P(1 + 0.12/12)^(12 * 2.5)
Simplifying further:
$11305 = P(1 + 0.01)^(30)
Now, let's solve for P, the principal amount.
Divide both sides of the equation by (1.01)^30:
$11305 / (1.01)^30 = P
Using a calculator:
P ≈ $8000.62
Therefore, Patrick's initial investment was approximately $8000.62.