PROBLEMS ON SIMPLE AND COMPOUND INTEREST

Problem 1 :

Calculate :

a) The simple interest earned on $2000 at 5% p.a. for 3 years.

b) Using a table, the compound interest earned on $2000 at 5% p.a. for 3 years.

Solution :

a) P = $2000, R = 5%, T = 3 years

Simple interest I = (P × T × R)/100

= (2000 × 3 × 5)/100

= 30000/100

= 300

So, simple interest is $300.

b) Amount = P(1 + R/100)^t

= 2000(1 + 0.05)³

= 2000(1.05)³

= 2000 × 1.157625

= 2315.25

Compound interest = Amount – Principal

= 2315.25 – 2000

= 315.25

So, compound interest is $315.25.

Problem 2 :

If $50,000 is invested at 9% p.a. compound interest, use a table to find:

a) The final amount after 2 years.

b) How much interest was earned in the 2 year period.

Solution :

a) P = $50000, R = 9% and T = 2 years

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

= 50000(1 + 0.09)²

= 50000(1.09)²

= 50000(1.1881)

= 59405

Compound interest = Amount – Principal

= 59405 – 50000

= 9405

So, final amount after 2 years is 9405.

a) P = $50000, R = 9% ==> 0.09 and T = 2 years

Simple interest I = (P × T × R)/100

= (50000 × 2 × 9)/100

= 900000/100

= 9000

So, interest was earned in the 2 year period is 9000.

Problem 3 :

Determine the interest earned for the following investments 

a. $4000 at 8% p.a. compound interest for 2 years.

b. $12000 at 6% p.a. compound interest for 3 years.

c. $500 at 3% p.a. compound interest for 3 years.

Solution :

a) P = $4000, R = 8%, T = 2 years

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

= 4000(1 + 0.08)²

= 4000(1.08)²

= 4000 × 1.1664

= 4665.6

Compound interest = Amount – Principal

= 4665.6 – 4000

= 665.6

So, compound interest is $665.6.

b) P = $12000, R = 6% and T = 3 years

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

= 12000(1 + 6/100)³

= 12000(1 + 0.06)³

= 12000(1.06)³

= 12000 × 1.191016

= 14292.192

Compound interest = Amount – Principal

= 14292.192 – 12000

= 2292.192

So, compound interest is $2292.192.

c) P = $500, R = 3% ==> 0.03, T = 3 years

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

= 500(1 + 3/100)³

= 500(1 + 0.03)³

= 500(1.03)³

= 500 × 1.092727

= 546.3635

Compound interest = Amount – Principal

= 546.3635 – 500

= 46.3635

So, compound interest is $46.3635.