Question

find the compound interest and total amount after 1 year if interest is compounded quarterly principal is 256 and rate of interest is 100% per annum find compound interest and total amount​

Answer 1

Answer:

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 quarterly (i.e., 3 months or, 4 times in a year) then the number of years (n) is 4 times (i.e., made 4n) and the rate of annual interest (r) is one-fourth (i.e., made r4). In such cases we use the following formula for compound interest when the interest is calculated quarterly.

If the principal = P, rate of interest per unit time = r4%, number of units of time = 4n, the amount = A and the compound interest = CI

Then

A = P(1 + r4100)4n

Here, the rate percent is divided by 4 and the number of years is multiplied by 4.

Therefore, CI = A - P = P{(1 + r4100)4n - 1}

Note:

A = P(1 + r4100)4n 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 + r4100)4n - 1} is the relation among the four quantities P, r, n and CI.

Step-by-step explanation:

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