What is the compound interest on 1400 compounded semi-annually for five years with a rate of 8%?
If you start with 100% of your $1,400, every half year, you add 4%, and will end up with 104%, or 1.04 times your money. So, for each half-year, you multiply 1.04, and you end up with an exponential equation. After doing this 10 times (twice a year for 5 years), you get:
1400*(1.04)^10 = 2072.34
In general the formula for compound interest is:
A = P (1 + r / n)Yn
where A is what you end up with, P is what you start with, r is the interest rate, n is number of times compounded per year, and Y is years.
Consider that Principal, P invested at a rate of R% per annual, so the interest earned in first year would be:
interest= P * R%*1= PR/100.
Then, at the end of one year, the amount of interests would be the original principal plus the interest earned, which is:
P+ PR/100= P(1+R/100)
If the person who invsted money into his account earned a compound interest, means an adding up of interests together to get a value, the principal amount would be P(1+R/100) sp o the interest earned in the second year would be:
The total amount of investments would be:
P(1+R/100)+P(1+R/100)R/100= P(1+R/100)(1+R/100)= P(1+R/100)^2.
The general formula would be A= P(1+R/100)^n
where A: amount, P: principal sm, R= rate of interest, and
n: number of interest periods.
Since we don't know what is the value of A, but we know that
P= $1400, R= 8% and n=5
so by the end of the fifth year, the total amount of investments made by the person would be:
The compounded interest would be:
Total amount of investments - principal sum of amount
= 1622.98- 1400