Simple Interest
Math MCQs

Question :    Linda had to pay $3551 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3551

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

$3551 = P (1 + 2% × 3)

⇒ $3551 = P (1 + ²/₁₀₀ × 3)

⇒ $3551 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3551 = P (1 + ⁶/₁₀₀)

⇒ $3551 = P (^{100 + 6}/₁₀₀)

⇒ $3551 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3551

⇒ P = ³⁵⁵¹/_¹⁰⁶/100

⇒ P = 3551 × ¹⁰⁰/₁₀₆

⇒ P = ^{3551 × 100}/₁₀₆

⇒ P = ³⁵⁵¹⁰⁰/₁₀₆

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3551, then the Principal = ¹⁰⁰/₁₀₆ × 3551

= ^{100 × 3551}/₁₀₆

= ³⁵⁵¹⁰⁰/₁₀₆

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(5) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?

(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.