Simple Interest
Math MCQs

Question :    Matthew had to pay $4452 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  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4452

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

$4452 = P (1 + 2% × 3)

⇒ $4452 = P (1 + ²/₁₀₀ × 3)

⇒ $4452 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4452 = P (1 + ⁶/₁₀₀)

⇒ $4452 = P (^{100 + 6}/₁₀₀)

⇒ $4452 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4452

⇒ P = ⁴⁴⁵²/_¹⁰⁶/100

⇒ P = 4452 × ¹⁰⁰/₁₀₆

⇒ P = ^{4452 × 100}/₁₀₆

⇒ P = ⁴⁴⁵²⁰⁰/₁₀₆

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4452, then the Principal = ¹⁰⁰/₁₀₆ × 4452

= ^{100 × 4452}/₁₀₆

= ⁴⁴⁵²⁰⁰/₁₀₆

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.

(4) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.

(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(6) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(8) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?