# Find Compound Interest when interest is compounded Quarterly

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To find compound interest when interest is compounded quarterly, we use the following formula :

A = P ( 1 + R/4 )4n and C.I. = A – P

Where, P = Principal
R = Rate of interest p.a (per annum i.e annually)
n = number of years.
Examples :

1) Find the compound interest on $320,000 for one year at the rate of 20% p.a., if the interest rate is compounded quarterly. Solution: Here, P =$320,000, R = 20% p.a. and n = 1 year.

∴ Amount after 1 year = P ( 1 + R/4 )4n

= 320,000 x ( 1 + 0.20/4 )4 x 1

= 320,000 x ( 1 + 0.05)4

= 320,000 x (1.05 )4

= 320,000 x 1.21550

= Rs. 388,962

∴ Compound interest = 388,962 – 320,000 = 68,962

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2)Ryan deposited $7500 in a bank which pays him 12% interest p.a. compounded quarterly. What is the amount which he receives after 9 months? Solution: Here, P =$ 7500, R = 12% p.a. and n = 9 months = 9/12 year = 3/4 year

∴ Amount after 9 months = P ( 1 + R/100 )4n

= 7500 x ( 1 + 0.12/4 )4n

= 7500 x ( 1 + 0.03 )4 x 3/4

= 7500 x ( 1.03)3

= 7500 x 1.092727

= $8195.45 ________________________________________________________________ 3)Jacob deposited$ 9000 in a bank which pays him 8% interest p.a. compounded quarterly. What is the amount which he receives after 6 months?

Solution:
Here, P = $9000, R = 8% p.a. and n = 6 months = 6/12 year = 1/2 year ∴ Amount after 6 months = P ( 1 + R/100 )4n = 9000 x ( 1 + 0.08/4 )4 x 1/2 = 9000 x ( 1 + 0.02 )2 = 9000 x ( 1.02)2 = 9363.6 =$ 9363.60

Compound Interest

Find Compound Interest when interest is compounded Half yearly
Find Compound Interest when interest is compounded Quarterly
Find CI when interest is compounded annually but Rates are different
Finding Principal
Finding Time Period of Investment
Finding Rate of Interest