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.

Problem 4 :

Tong loaned Jody $50 for a month. He charged 5% simple interest for the month. How much did Jody have to pay Tong?

Solution :

Simple interest = PTR/100

Loan amount = $50

Interest rate = 5%

Time = 1/12

= (50 x 1/12 x 5)/100

= 0.20

Amount to be paid = 50 + 0.20

= 50.20

Problem 5 :

Jessica’s grandparents gave her $2000 for college to put in a savings account until she starts college in four years. Her grandparents agreed to pay her an additional 7.5% simple interest on the $2000 for every year.

How much extra money will her grandparents give her at the end of four years?

Solution :

P = 2000

R = 7.5%

N = 4

Simple interest = PTR/100

= (2000 x 4 x 7.5)/100

= 600

At the end of four years, her grandparents will give $600.

Problem 6 :

Mai put $4250 in the bank at 4.4% interest compounded annually. How much was in her account after 7 years?

Solution :

P = $4250, R = 4.4%, T = 7 years

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

= 4250(1 + 0.044)⁷

= 4250(1.3517)

= 5744.72

Approximately 5745 is the amount he will receive after 7 years.

Problem 7 :

What is the difference in the amount of money in the bank after five years if $2500 is invested at 3.2% interest compounded annually or at 2.9% interest compounded annually?

Solution :

Investing 2500 at the rate of 3.2% :

P = $2500, R = 3.2%, T = 5 years

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

= 2500(1 + 0.032)⁵

= 2500(1.032)⁵

= 2500(1.170)

= 2925

Investing 2500 at the rate of 2.9% :

P = $2500, R = 2.9%, T = 5 years

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

= 2500(1 + 0.029)⁵

= 2500(1.029)⁵

= 2500(1.153)

= 2882.5

Difference between the amount = 2925 - 2882.5

= $42.5

Problem 8 :

Ronna was listening to her parents talking about what a good deal compounded interest was for a retirement account. She wondered how much money she would have if she invested $2000 at age 20 at 2.8% annual interest compounded quarterly (four times each year) and left it until she reached age 65. Determine what the value of the $2000 would become.

Solution :

P = 2000, R = 2.8%, T= 65 - 20 ==> 45

Compounding quarterly :

Amount = P(1 + R%/4)^4t

= 2000(1 + 0.028/4)⁴⁽⁴⁵⁾

= 2000(1 + 0.007)¹⁸⁰

= 2000(1 + 0.007)¹⁸⁰

= 2000(1.007)¹⁸⁰

= 2000(3.509)

= 2000(3.51)

= 7020