If you have 4000 birr today and you want to deposit it in a bank that bears 5% compounded quarterly for 3 years, how much birr you will have at maturity?
At maturity, you will have 4,619.45 birr.
To calculate the amount you will have at maturity, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount at maturity
P = the principal amount (4000 birr in this case)
r = the annual interest rate (5% or 0.05)
n = the number of times that interest is compounded per year (quarterly, so 4)
t = the number of years
Plugging in the given values:
A = 4000(1 + 0.05/4)^(4*3)
Next, we simplify the equation:
A = 4000(1 + 0.0125)^12
Now, we calculate the exponential part of the equation:
A = 4000(1.0125)^12
Using a calculator, we find:
A ≈ 4000 * 1.160984
A ≈ 4643.94
Therefore, you will have approximately 4643.94 birr at maturity.
To calculate the maturity amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = the maturity amount
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given that the principal amount (P) is 4000 birr, the interest rate (r) is 5% (0.05 as a decimal), the interest is compounded quarterly (n = 4), and the time period (t) is 3 years, we can substitute these values into the formula and solve for A.
A = 4000 * (1 + 0.05/4)^(4 * 3)
Now, let's calculate this in steps using the formula:
Step 1: Calculate the bracketed term inside the exponent.
(1 + 0.05/4) = 1.0125
Step 2: Calculate the exponent.
4 * 3 = 12
Step 3: Calculate the final maturity amount.
A = 4000 * (1.0125)^12
By evaluating this expression, the maturity amount comes out to be approximately 4622.60 birr.