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) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(4) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

(5) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.