Simple Interest
Math MCQs

Question :    If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4752

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$4752 = P (1 + 2% × 4)

⇒ $4752 = P (1 + ²/₁₀₀ × 4)

⇒ $4752 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4752 = P (1 + ⁸/₁₀₀)

⇒ $4752 = P (^{100 + 8}/₁₀₀)

⇒ $4752 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4752

⇒ P = ⁴⁷⁵²/_¹⁰⁸/100

⇒ P = 4752 × ¹⁰⁰/₁₀₈

⇒ P = ^{4752 × 100}/₁₀₈

⇒ P = ⁴⁷⁵²⁰⁰/₁₀₈

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4752, then the Principal = ¹⁰⁰/₁₀₈ × 4752

= ^{100 × 4752}/₁₀₈

= ⁴⁷⁵²⁰⁰/₁₀₈

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(2) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.

(8) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?