Question

When the interest is compounded half-yearly, How many conversion periods are there in 3 years?​

Answer 1

Answer:

We will learn how to use the formula for calculating the compound interest when interest is compounded half-yearly.

Computation of compound interest by using growing principal becomes lengthy and complicated when the period is long. If the rate of interest is annual and the interest is compounded half-yearly (i.e., 6 months or, 2 times in a year) then the number of years (n) is doubled (i.e., made 2n) and the rate of annual interest (r) is halved (i.e., made r2r2).  In such cases we use the following formula for compound interest when the interest is calculated half-yearly.

If the principal = P, rate of interest per unit time = r2r2%, number of units of time = 2n, the amount = A and the compound interest = CI

Then

A = P(1 + r2100r2100)2n2n

Here, the rate percent is divided by 2 and the number of years is multiplied by 2

Therefore,  CI = A - P = P{(1 + r2100r2100)2n2n - 1}

Note:

A = P(1 + r2100r2100)2n2n is the relation among the four quantities P, r, n and A.

Given any three of these, the fourth can be found from this formula.

CI = A - P = P{(1 + r2100r2100)2n2n - 1} is the relation among the four quantities P, r, n and CI.

Given any three of these, the fourth can be found from this formula.