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 if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(3) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

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

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?

(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?