COMPOUND INTEREST EXAMPLE PROBLEMS

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.