Find the amount if principal is 1,25,000, rate is 8%
p.a. compounded quarterly for 5/4 years
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Compound Interest when Interest is Compounded Quarterly
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We will learn how to use the formula for calculating the compound interest when interest is compounded quarterly.
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.
Given any three of these, the fourth can be found from this formula.
Word problems on compound interest when interest is compounded quarterly:
1. Find the compound interest when $1,25,000 is invested for 9 months at 8% per annum, compounded quarterly.
Solution:
Here, P = principal amount (the initial amount) = $ 1,25,000
Rate of interest (r) = 8 % per annum
Number of years the amount is deposited or borrowed for (n) = 912 year = 34 year.
Therefore,
The amount of money accumulated after n years (A) = P(1 + r4100)4n
= $ 1,25,000 (1 + 84100)4∙34
= $ 1,25,000 (1 + 2100)3
= $ 1,25,000 (1 + 150)3
= $ 1,25,000 × (5150)3
= $ 1,25,000 × 5150 × 5150 × 5150
= $ 1,32,651
Therefore, compound interest $ (1,32,651 - 1,25,000) = $ 7,651.