Simple Interest
MCQs Math


Question:     Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.


Correct Answer  $4050

Solution And Explanation

Solution

Given,

Amount (A) = $4293

Rate of Simple Interest (R) = 2%

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

$4293 = P (1 + 2% × 3)

⇒ $4293 = P (1 + 2/100 × 3)

⇒ $4293 = P (1 + 2 × 3/100)

⇒ $4293 = P (1 + 6/100)

⇒ $4293 = P (100 + 6/100)

⇒ $4293 = P × 106/100

⇒ P × 106/100 = $4293

⇒ P = 4293/106/100

⇒ P = 4293 × 100/106

⇒ P = 4293 × 100/106

⇒ P = 429300/106

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 = 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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/106

∴ If the Amount is 4293, then the Principal = 100/106 × 4293

= 100 × 4293/106

= 429300/106

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer


Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(3) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(6) 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.

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

(8) Joshua had to pay $5488 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 Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?

(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.


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