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) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(4) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?