Simple Interest
MCQs Math


Question:     How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?


Correct Answer  $7350

Solution And Explanation

Solution

Given,

Amount (A) = $8820

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

$8820 = P (1 + 4% × 5)

⇒ $8820 = P (1 + 4/100 × 5)

⇒ $8820 = P (1 + 4 × 5/100)

⇒ $8820 = P (1 + 20/100)

⇒ $8820 = P (100 + 20/100)

⇒ $8820 = P × 120/100

⇒ P × 120/100 = $8820

⇒ P = 8820/120/100

⇒ P = 8820 × 100/120

⇒ P = 8820 × 100/120

⇒ P = 882000/120

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8820, then the Principal = 100/120 × 8820

= 100 × 8820/120

= 882000/120

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer


Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(2) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(6) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

(7) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

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

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.


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