Simple Interest
Math MCQs

Question :    If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $4140

Rate of Simple Interest (R) = 5%

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

$4140 = P (1 + 5% × 4)

⇒ $4140 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4140 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4140 = P (1 + ²⁰/₁₀₀)

⇒ $4140 = P (^{100 + 20}/₁₀₀)

⇒ $4140 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4140

⇒ P = ⁴¹⁴⁰/_¹²⁰/100

⇒ P = 4140 × ¹⁰⁰/₁₂₀

⇒ P = ^{4140 × 100}/₁₂₀

⇒ P = ⁴¹⁴⁰⁰⁰/₁₂₀

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4140, then the Principal = ¹⁰⁰/₁₂₀ × 4140

= ^{100 × 4140}/₁₂₀

= ⁴¹⁴⁰⁰⁰/₁₂₀

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(2) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(5) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

(9) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?