Simple Interest
MCQs Math


Question:     How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?


Correct Answer  $6950

Solution And Explanation

Solution

Given,

Amount (A) = $8340

Rate of Simple Interest (R) = 4%

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

$8340 = P (1 + 4% × 5)

⇒ $8340 = P (1 + 4/100 × 5)

⇒ $8340 = P (1 + 4 × 5/100)

⇒ $8340 = P (1 + 20/100)

⇒ $8340 = P (100 + 20/100)

⇒ $8340 = P × 120/100

⇒ P × 120/100 = $8340

⇒ P = 8340/120/100

⇒ P = 8340 × 100/120

⇒ P = 8340 × 100/120

⇒ P = 834000/120

⇒ P = $6950

Thus, the sum borrowed (P) = $6950 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/120

∴ If the Amount is 8340, then the Principal = 100/120 × 8340

= 100 × 8340/120

= 834000/120

= 6950

Thus, Principal = $6950

Thus, the sum borrowed = $6950 Answer


Similar Questions

(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(8) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.


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