Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $7680

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

$7680 = P (1 + 4% × 5)

⇒ $7680 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7680 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7680 = P (1 + ²⁰/₁₀₀)

⇒ $7680 = P (^{100 + 20}/₁₀₀)

⇒ $7680 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7680

⇒ P = ⁷⁶⁸⁰/_¹²⁰/100

⇒ P = 7680 × ¹⁰⁰/₁₂₀

⇒ P = ^{7680 × 100}/₁₂₀

⇒ P = ⁷⁶⁸⁰⁰⁰/₁₂₀

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 7680, then the Principal = ¹⁰⁰/₁₂₀ × 7680

= ^{100 × 7680}/₁₂₀

= ⁷⁶⁸⁰⁰⁰/₁₂₀

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(7) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(9) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?