find the amount and the compoud interest on r 12800 for 1year at 15/2% per annum, compounded semi- annually.
14792
amount =14792 ci=1992
compound interest, A = p (1 + (r/n) )^(nt)
where p=pricipal, r=rate, n=number of compounding periods t=years
A = 12800 ( 1 + (0.075/2))^2
A = 13778
To find the compound interest and the amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The future value or the amount
P = The principal amount
r = The annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
Given:
P = $12,800
r = 15/2% = 15/2/100 = 0.075 (convert to decimal)
n = 2 (compounded semi-annually)
t = 1 year
Now, let's substitute the values into the formula:
A = 12800(1 + 0.075/2)^(2*1)
A = 12800(1 + 0.0375)^(2)
A = 12800(1.0375)^(2)
A = 12800 * 1.07681640625
A ≈ $13,802.93 (rounded to two decimal places)
Therefore, the amount after 1 year will be approximately $13,802.93.
To find the compound interest, we subtract the principal amount from the amount:
Compound Interest = A - P
Compound Interest = 13802.93 - 12800
Compound Interest ≈ $1002.93 (rounded to two decimal places)
Therefore, the compound interest on $12,800 for 1 year at a rate of 15/2% compounded semi-annually is approximately $1002.93.