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) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.

(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(4) 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.

(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.