Simple Interest
MCQs Math


Question:     How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?


Correct Answer  $7750

Solution And Explanation

Solution

Given,

Amount (A) = $8525

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$8525 = P (1 + 2% × 5)

⇒ $8525 = P (1 + 2/100 × 5)

⇒ $8525 = P (1 + 2 × 5/100)

⇒ $8525 = P (1 + 10/100)

⇒ $8525 = P (100 + 10/100)

⇒ $8525 = P × 110/100

⇒ P × 110/100 = $8525

⇒ P = 8525/110/100

⇒ P = 8525 × 100/110

⇒ P = 8525 × 100/110

⇒ P = 852500/110

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/110

∴ If the Amount is 8525, then the Principal = 100/110 × 8525

= 100 × 8525/110

= 852500/110

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer


Similar Questions

(1) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.

(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(9) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(10) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?


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