Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $7200

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

$7200 = P (1 + 4% × 5)

⇒ $7200 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7200 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7200 = P (1 + ²⁰/₁₀₀)

⇒ $7200 = P (^{100 + 20}/₁₀₀)

⇒ $7200 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7200

⇒ P = ⁷²⁰⁰/_¹²⁰/100

⇒ P = 7200 × ¹⁰⁰/₁₂₀

⇒ P = ^{7200 × 100}/₁₂₀

⇒ P = ⁷²⁰⁰⁰⁰/₁₂₀

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 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 7200, then the Principal = ¹⁰⁰/₁₂₀ × 7200

= ^{100 × 7200}/₁₂₀

= ⁷²⁰⁰⁰⁰/₁₂₀

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(6) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(10) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.