WORD PROBLEMS ON SIMPLE INTEREST

Problem 1 :

Find the simple interest rate (to the nearest per cent) which will allow €2500 to earn €675 interest in 3 years.

Solution:

Given, P = 2500, T = 3 years, SI = 675

Problem 2 :

What sum of money would you have to invest for 5 years at 11% simple interest to produce interest at €3080?

Solution:

Given, SI = 3080, T = 5 years, R = 11%

Problem 3 :

For how many years would $8000 have to be invested at 11 1/2% simple interest to produce €5520 interest?

Solution:

Given, P = 8000, SI = 5520, R = 11 1/2%

Problem 4 :

What simple interest rate would allow €6000 to grow to an amount €14550 in 10 years?

Solution:

Given, P = 6000, A = 14550, T = 10 years

A = P (1 + rt)

14550 = 6000 (1 + 10r)

14550 = 6000 + 60000r

14550 - 6000 = 60000r

8550 = 60000r

Problem 5 :

What simple interest would $8000 earn in 3 months if the rate of interest is 11 1/4 % pa?

Solution:

Given, P = 8000, T = 3 months = 3/12 years

T = 0.25 years, R = 11 1/4% = 45/4%

Problem 6 :

A building society pays interest daily. If an amount of $1564 were invested at 5.5% pa, how much simple interest would be earned in:

i. 1 day?     ii. 3 days?     iii. 29 days?

Solution:

i. Given, P = $1564, R = 5.5%, T = 1 day = 1/365 year

ii. Given, P = $1564, R = 5.5%, T = 3 days = 3/365 year

iii.  Given, P = $1564, R = 5.5%, T = 29 days = 29/365 year

Problem 7 :

After 7 years at 3% simple interest per year, your savings account earns $63.

a. What is the principal?

b. How much money do you have left after buying the video game system?

Solution :

a)

I = PTR / 100

T = 7 years, R = 3% and I = 63

63 = (P x 7 x 3)/100

6300 = 21P

P = 6300/21

P = 300

So, the required principal should be $300.

b)

Amount = Principal + interest

= 300 + 63

= 363

After purchasing the video game system, the amount remaining = 363 - 350

= 13

Problem 8 :

The owners of a company want to invest $12,000 for 4 years.

a) Which account should they choose? Explain.

• Account A earns 5% simple interest per year.
• Account B earns 5% interest compounded annually.

b) How much more do they earn by choosing the better account?

Solution :

a) P = 12000, T = 4, R = 5%

Interest = PTR/100

= (12000 x 4 x 5)/100

= (120 x 4 x 5)

= $2400

Compound interest :

A = P (1 + r)^t

= 12000(1 + 0.05)⁴

= 12000(1.05)⁴

= 14586

Interest = Amount - principal

= 14586 - 12000

= 2586

b) Investing amount in compound interest is greater.

Problem 9 :

A music company offers a loan to buy a drum set for $1500. What is the monthly payment?

Solution :

P = 1500

R = 2

T = 11.8%

Interest = PTR/100

Interest = (1500 x 2 x 11.8)/100

= 354

The loan amount along with the interest = 1500 + 354

= 1854

Monthly payment = 1854/12

= 154.5

Problem 10 :

How many years will it take for $2000 to double at a simple interest rate of 8%? Explain how you found your answer.

Solution :

P = 2000, T = ?, R = 8%

Interest earned for one year = (2000 x 1 x 8)/100

= 20 x 8

= 160

= 2000 / 160

= 12.5 years.