Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7440

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

$7440 = P (1 + 4% × 5)

⇒ $7440 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7440 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7440 = P (1 + ²⁰/₁₀₀)

⇒ $7440 = P (^{100 + 20}/₁₀₀)

⇒ $7440 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7440

⇒ P = ⁷⁴⁴⁰/_¹²⁰/100

⇒ P = 7440 × ¹⁰⁰/₁₂₀

⇒ P = ^{7440 × 100}/₁₂₀

⇒ P = ⁷⁴⁴⁰⁰⁰/₁₂₀

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 7440, then the Principal = ¹⁰⁰/₁₂₀ × 7440

= ^{100 × 7440}/₁₂₀

= ⁷⁴⁴⁰⁰⁰/₁₂₀

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.