Simple Interest
Math MCQs

Question :    If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5640

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

$5640 = P (1 + 5% × 4)

⇒ $5640 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5640 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5640 = P (1 + ²⁰/₁₀₀)

⇒ $5640 = P (^{100 + 20}/₁₀₀)

⇒ $5640 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5640

⇒ P = ⁵⁶⁴⁰/_¹²⁰/100

⇒ P = 5640 × ¹⁰⁰/₁₂₀

⇒ P = ^{5640 × 100}/₁₂₀

⇒ P = ⁵⁶⁴⁰⁰⁰/₁₂₀

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 5640, then the Principal = ¹⁰⁰/₁₂₀ × 5640

= ^{100 × 5640}/₁₂₀

= ⁵⁶⁴⁰⁰⁰/₁₂₀

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(6) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?

(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?