Simple Interest
MCQs Math


Question:     Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.


Correct Answer  $3050

Solution And Explanation

Solution

Given,

Amount (A) = $3416

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$3416 = P (1 + 4% × 3)

⇒ $3416 = P (1 + 4/100 × 3)

⇒ $3416 = P (1 + 4 × 3/100)

⇒ $3416 = P (1 + 12/100)

⇒ $3416 = P (100 + 12/100)

⇒ $3416 = P × 112/100

⇒ P × 112/100 = $3416

⇒ P = 3416/112/100

⇒ P = 3416 × 100/112

⇒ P = 3416 × 100/112

⇒ P = 341600/112

⇒ 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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 3416, then the Principal = 100/112 × 3416

= 100 × 3416/112

= 341600/112

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer


Similar Questions

(1) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.

(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(4) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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

(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(8) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(10) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.


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