# COMPOUND INTEREST EXAMPLE PROBLEMS

Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.

Amount (A) = P(1 + R/100)t

Interest = Amount - Principal

Here P = principal, R = rate of interest and t = time of investment

Problem 1 :

a) What will an investment of \$3000 at 10% p.a. Compound interest amount to after 3 years?

b) What part of this is interest?

Solution :

P= \$3000, R = 10% ==> 0.10 and T = 3 years

a)  Amount A = P(1 + R/100)t

= 3000(1 + 0.1)3

= 3000(1.1)3

= 3000(1.331)

= \$3993

b) Compound interest = Amount – Principal

= 3993 – 3000

= \$993

So, interest is \$993.

Problem 2 :

How much compound interest is earned by investing \$20,000 for 4 years at 12% p.a.?

Solution :

P= \$20000, R = 12% and T = 4 years

Amount A = P(1 + R/100)t

= 20000(1 + 0.12)4

= 20000(1.12)4

= 20000(1.57351936)

= 31470.39

Compound interest = Amount – Principal

= 31470.39 – 20000

= 11470.39

So, compound interest is \$11470.39.

Problem 3 :

\$5000 is invested for 2 years at 10% p.a. What will this investment amount to if the interest is calculated as :

a) Simple interest

b) Compound interest?

Solution :

P= \$5000, R = 10% ==> 0.10 and T = 2 year

a)  Simple interest I = (P × T × R)/100

= (5000 × 2 × 10)/100

= 100000/100

= 1000

So, simple interest is \$1000.

Total amount = P + I

= 5000 + 1000

= 6000

So, total amount is £6000.

b) Compound interest = P(1 + R/100)t

= 5000(1 + 0.1)2

= 5000(1.1)2

= 5000(1.21)

= \$6050

So, compound interest is \$6050.

Problem 4 :

a) What will an investment of \$30,000 at 10% p.a. Compound interest amount to after 4 years?

b) What part of this is interest?

Solution :

P= \$30000, R = 10% and T = 4 years

a) Amount A = P(1 + R/100)t

= 30000(1 + 0.1)4

= 30000(1.1)4

= 30000(1.4641)

= \$43923

b) Compound interest = Amount – Principal

= 43923 – 30000

= \$13923

So, interest is \$13923.

Problem 5 :

How much compound interest is earned by investing €80,000 at 9% p.a. over a 3 year period?

Solution :

Principal amount P= \$80000

Rate R = 9%

Time T= 3 years

Amount A = P(1 + R/100)t

= 80000(1 + 0.09)3

= 80000(1.09)3

= 80000(1.295029)

= 103602.32

Compound interest = Amount – Principal

= 103602.32 – 80000

= 23602.32

So, compound interest is \$23602.32.

Problem 6 :

\$6000 is invested for 2 years at 15% p.a. What will this investment amount to if the interest is calculated as :

a) Simple interest

b) Compound interest?

Solution :

P= \$6000, R = 15% ==> 0.15 and T = 2 years

a) Simple interest = (P × T × R)/100

= 6000 × 2 × 0.15

= 1800

So, simple interest is \$1800.

Total amount = P + I

= 1800 + 6000

= 7800

So, total amount is \$7800.

b)  Compound interest = P(1 + R/100)t

= 6000(1 + 0.15)2

= 6000(1.15)2

= 6000(1.3225)

= 7935

So, compound interest is \$7935.

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