If the amount of money was invested before 10 years at a rate of 4% per year, compounded quarterly to get 30000birr. Then what amount of money was invested?
To find the initial investment amount, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount (30000 birr)
P = Principal amount (initial investment)
r = Interest rate per year (4% or 0.04)
n = Number of times interest is compounded per year (quarterly, so 4 times)
t = Number of years (10)
Plugging in the given values into the formula:
30000 = P(1 + 0.04/4)^(4*10)
Simplifying:
30000 = P(1 + 0.01)^(40)
30000 = P(1.01)^40
Now, we need to solve for P:
30000 / (1.01)^40 = P
P ≈ 22428.48
Therefore, the initial investment amount was approximately 22,428.48 birr.
To find the initial amount of money invested, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (30000 birr in this case)
P = the principal (initial amount invested)
r = the annual interest rate (4% or 0.04 in decimal form)
n = the number of times the interest is compounded per year (quarterly means 4 times per year)
t = the number of years (10 years in this case)
Substituting the values into the formula, we have:
30000 = P(1 + 0.04/4)^(4*10)
Simplifying the equation:
30000 = P(1 + 0.01)^(40)
30000 = P(1.01)^40
Now, let's solve for P:
P = 30000 / (1.01)^40
Using a calculator, we find:
P ≈ 19436.73 birr
Therefore, approximately 19436.73 birr was initially invested.