Simple Interest
MCQs Math


Question:     Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.


Correct Answer  $4500

Solution And Explanation

Solution

Given,

Amount (A) = $4905

Rate of Simple Interest (R) = 3%

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

$4905 = P (1 + 3% × 3)

⇒ $4905 = P (1 + 3/100 × 3)

⇒ $4905 = P (1 + 3 × 3/100)

⇒ $4905 = P (1 + 9/100)

⇒ $4905 = P (100 + 9/100)

⇒ $4905 = P × 109/100

⇒ P × 109/100 = $4905

⇒ P = 4905/109/100

⇒ P = 4905 × 100/109

⇒ P = 4905 × 100/109

⇒ P = 490500/109

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/109

∴ If the Amount is 4905, then the Principal = 100/109 × 4905

= 100 × 4905/109

= 490500/109

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer


Similar Questions

(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(2) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.

(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(6) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.


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