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) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.