Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $7080

Rate of Simple Interest (R) = 4%

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

$7080 = P (1 + 4% × 5)

⇒ $7080 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7080 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7080 = P (1 + ²⁰/₁₀₀)

⇒ $7080 = P (^{100 + 20}/₁₀₀)

⇒ $7080 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7080

⇒ P = ⁷⁰⁸⁰/_¹²⁰/100

⇒ P = 7080 × ¹⁰⁰/₁₂₀

⇒ P = ^{7080 × 100}/₁₂₀

⇒ P = ⁷⁰⁸⁰⁰⁰/₁₂₀

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 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 7080, then the Principal = ¹⁰⁰/₁₂₀ × 7080

= ^{100 × 7080}/₁₂₀

= ⁷⁰⁸⁰⁰⁰/₁₂₀

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(4) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?

(6) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.