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 Simple Interest Questions

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FACTS  AND  FORMULAE  FOR  SIMPLE  INTEREST  QUESTIONS

 

 

1. Principal: The money borrowed or lent out for a certain period is called the principal or the sum.

 

2. Interest: Extra money paid for using other's money is called interest

 

3. Simple Interest (S.I.) : If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then,

(i)  S.I=P×T×R100

(ii)  P=100×S.IR×T ; R=100×S.IP×T and T=100×S.IP×R

Q:

An amount of 5,000 is invested at a fixed rate of 8 per cent per annum. What amount will be the value of the investment in five years time, if the interest is compounded every six months?

A) 7401.22 B) 3456
C) 4567 D) 7890
 
Answer & Explanation Answer: A) 7401.22

Explanation:

With slight modifications, the basic formula can be made to deal with compounding at intervals other than annually.

 

Since the compounding is done at six-monthly intervals, 4 per cent (half of 8 per cent) will be added to the value on each occasion.

 

Hence we use r = 0.04. Further, there will be ten additions of interest during the five years, and so n = 10. The formula now gives:

 

V = P(1 + r)10 = 5,000 x (1.04)10 = 7,401.22

 

Thus the value in this instance will be £7,401.22.

 

In a case such as this, the 8 per cent is called a nominal annual

 

rate, and we are actually referring to 4 per cent per six months.

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Q:

A sum of Rs. 10,000 is lent partly at 6% and the remaining at 10% p.a. If the yearly interest on the average is 9.2%, the money lent at 10% is:-

A) Rs. 8000 B) Rs. 8500
C) Rs. 5000 D) Rs. 2000
 
Answer & Explanation Answer: A) Rs. 8000

Explanation:

Let the amount at 6% be x
Amount at 10% be (10000 –x)
At 9.2 % interest, SI = 10000 X 9.2 X 1/100 = 920
Amount = 10920
⇒ 6x/100 + (10000 – x)10/100 = 920
⇒ 6x – 10x + 100000 = 92000
⇒ 4x = 8000
⇒ x = 2000
Money lent at 10 % = 10000 – 2000 = 8000

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Q:

A bank offers 9% p.a. simple interest on an investment. At the end of 4 years the interest earned was $215. How much was invested?

A) 597.22 B) 345
C) 456 D) 378
 
Answer & Explanation Answer: A) 597.22

Explanation:

I = (p x r x t)/100

 

 

 

 

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Q:

The difference between the interests earned when Rs. P is invested for four years in a scheme offering 9% p.a. Simple interest and when the same sum (Rs P) is invested for two years in another scheme offering 12% p.a. simple interest, is Rs 480. What is the value of P?

A) 2000 B) 3500
C) 2500 D) 4000
 
Answer & Explanation Answer: D) 4000

Explanation:

p=(p*4*9)/100-(p*2*12)/100 = 480

=12p/100=480

p=4000

 

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Q:

If there is a total of 104 weekly instalments and a thirddeposit, find the interest charged

A) 237.55 B) 337
C) 443 D) 334
 
Answer & Explanation Answer: A) 237.55

Explanation:

Cash price = $3695

Deposit =1/3 of $3695 = $1231.67

Loan amount = $3695.00 − $1231.67 = $2463.33

Total cost of loan = $25.97 × 104= $2700.88

 

Interest charged = total amount − loan
I = A − P
= 2700.88 − 2463.33
= 237.55

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Q:

Find the principal which yields $25,000 when invested at 3% annually for 20 years.

A) 13841.89 B) 14821
C) 13468 D) 57389
 
Answer & Explanation Answer: A) 13841.89

Explanation:

P=F1+in

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Q:

loan of $15 000 is taken out. If the interest rate on the loan is 7%, how much interest is due and what is the amount repaid if the loan was taken out on April 7 and is due in seven months

A) 13615.52 B) 14615.52
C) 15615.52 D) 16615.52
 
Answer & Explanation Answer: C) 15615.52

Explanation:

I = prt = [15000 × 0.07 × (214/365) ]=615.52

Future value, S = P + I = $15 000 + $615.52 = $15 615.52

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Q:

A loan of $15 000 is taken out. If the interest rate on the loan is 7%, how much interest is due and what is the amount repaid if the loan is due in seven months

A) 15612.50 B) 14612.50
C) 13612.50 D) 17612.50
 
Answer & Explanation Answer: A) 15612.50

Explanation:

We have P = 15 000, r = 0.07 and since the actual date the loan was taken out
is not given, we use t =7/12

I = Prt=$15 000* 0.07* 7/12 = $612.50

Amount repaid = Future or accumulated value,

S = P + I = $15 000 + $612.50 = $15 612.50

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