Calculate the amount when the principal is Rs.12550 and the rate of interest is 9% semi annually and the time is 2.5 years .
Compounded semi-annually(see similar problems).
A = Po(1+r)^n.
r = 0.09/2 = 0.045.
n = 2comp./ yr. * 2.5yrs = 5 compounding periods.
A = 12,550(1+0.045)^5 = 15,639.58
.09/2 = .045
.045 * 12550 * 5 = total interest if simple interest
To calculate the amount when the principal is Rs. 12550, the rate of interest is 9% semiannually, and the time is 2.5 years, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = Amount
P = Principal
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
Let's calculate step by step:
Step 1: Convert the annual interest rate to a decimal
Since the rate of interest is 9%, we divide it by 100:
r = 9/100 = 0.09
Step 2: Calculate the number of times interest is compounded per year
Since the interest is compounded semiannually (twice a year):
n = 2
Step 3: Calculate the amount using the formula
A = 12550 * (1 + 0.09/2)^(2*2.5)
Let's calculate the values in the formula:
A = 12550 * (1 + 0.045)^(5)
A = 12550 * (1.045)^(5)
A = 12550 * 1.234489322025
A ≈ 15480.53 (rounded to two decimal places)
Therefore, the amount when the principal is Rs. 12550, the interest rate is 9% semiannually, and the time is 2.5 years would be approximately Rs. 15480.53.
To calculate the final amount when the principal, rate of interest, and time are given, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t),
where:
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
In this case, the principal amount (P) is Rs. 12550, the rate of interest (r) is 9% (or 0.09 as a decimal), the time (t) is 2.5 years, and the interest is compounded semi-annually, so the number of times interest is compounded per year (n) is 2.
Plugging the values into the formula, we get:
A = 12550(1 + 0.09/2)^(2*2.5)
Simplifying the equation gives:
A = 12550(1 + 0.045)^(5)
Calculating further:
A = 12550(1.045)^(5)
A ≈ 12550 * 1.2366
A ≈ 15553.73
Therefore, the amount, after 2.5 years, with a principal of Rs. 12550 at a semi-annual interest rate of 9%, will be approximately Rs. 15553.73.