Rate Compounded Annually Or Half Yearly (Semi Annually)

• Conversion Period: Time period and rate when interest not compounded annually The time period after which the interest is added each time to form a new principal is called the conversion period.

Rate Compounded Annually Or Half Yearly (Semi-Annually):

Time period and rate when interest not compounded annually The time period after which the interest is added each time to form a new principal is called the conversion period.

i) When compound interest is compounded annually,

Amount when interest is compounded annually = `"P"( 1 + "R"/100)^n`; 

P is principal, R is rate of interest, n is time period

P = Rs. 100 at 10% per annum compounded annually
The time period taken is 1 year 

I = ₹ `(100 xx 10 xx 1)/100` = Rs. 10

A = Rs. 100 + Rs. 10

A = Rs. 110.

ii) When compound interest is compounded Semi-annually,

When the interest is compounded half-yearly, there are two conversion periods in a year each after 6 months. In such situations, the half-yearly rate will be half of the annual rate.

Amount when interest is compounded half-yearly

= `"P"( 1 + "R"/200)^(2n)        .......{"R"/2 "is half-yearly rate and"
, 2n = "number of half-years"`

iii) When compound interest is compounded quarterly,

In this case, there are 4 conversion periods in a year and the quarterly rate will be one-fourth of the annual rate.

Amount when interest is compounded quarterly,

= `"P"(1 + "R"/400)^(4n)       ........{ "R"/4 "is half-yearly rate and, 4n = number of half-years"’`