# Find Compound Interest when interest is compounded Quarterly

To find compound interest when interest is compounded quarterly, we use the following formula :**A = P ( 1 + R/4 )**

^{4n}and C.I. = A – PWhere, 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

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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

• 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