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) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(5) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.