Simple Interest
MCQs Math


Question:     If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.


Correct Answer  $3050

Solution And Explanation

Solution

Given,

Amount (A) = $3294

Rate of Simple Interest (R) = 2%

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

$3294 = P (1 + 2% × 4)

⇒ $3294 = P (1 + 2/100 × 4)

⇒ $3294 = P (1 + 2 × 4/100)

⇒ $3294 = P (1 + 8/100)

⇒ $3294 = P (100 + 8/100)

⇒ $3294 = P × 108/100

⇒ P × 108/100 = $3294

⇒ P = 3294/108/100

⇒ P = 3294 × 100/108

⇒ P = 3294 × 100/108

⇒ P = 329400/108

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/108

∴ If the Amount is 3294, then the Principal = 100/108 × 3294

= 100 × 3294/108

= 329400/108

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer


Similar Questions

(1) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(3) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(7) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?


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