Simple Interest
MCQs Math


Question:     If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


Correct Answer  $3150

Solution And Explanation

Solution

Given,

Amount (A) = $3528

Rate of Simple Interest (R) = 3%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$3528 = P (1 + 3% × 4)

⇒ $3528 = P (1 + 3/100 × 4)

⇒ $3528 = P (1 + 3 × 4/100)

⇒ $3528 = P (1 + 12/100)

⇒ $3528 = P (100 + 12/100)

⇒ $3528 = P × 112/100

⇒ P × 112/100 = $3528

⇒ P = 3528/112/100

⇒ P = 3528 × 100/112

⇒ P = 3528 × 100/112

⇒ P = 352800/112

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 3528, then the Principal = 100/112 × 3528

= 100 × 3528/112

= 352800/112

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer


Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.

(10) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©