Simple Interest
Math MCQs

Question :    How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Amount (A) = $5940

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$5940 = P (1 + 2% × 5)

⇒ $5940 = P (1 + ²/₁₀₀ × 5)

⇒ $5940 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5940 = P (1 + ¹⁰/₁₀₀)

⇒ $5940 = P (^{100 + 10}/₁₀₀)

⇒ $5940 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5940

⇒ P = ⁵⁹⁴⁰/_¹¹⁰/100

⇒ P = 5940 × ¹⁰⁰/₁₁₀

⇒ P = ^{5940 × 100}/₁₁₀

⇒ P = ⁵⁹⁴⁰⁰⁰/₁₁₀

⇒ P = $5400

Thus, the sum borrowed (P) = $5400 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 5940, then the Principal = ¹⁰⁰/₁₁₀ × 5940

= ^{100 × 5940}/₁₁₀

= ⁵⁹⁴⁰⁰⁰/₁₁₀

= 5400

Thus, Principal = $5400

Thus, the sum borrowed = $5400 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(6) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(10) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.