Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $6500

Rate of Simple Interest (R) = 5%

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

$6500 = P (1 + 5% × 5)

⇒ $6500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6500 = P (1 + ²⁵/₁₀₀)

⇒ $6500 = P (^{100 + 25}/₁₀₀)

⇒ $6500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6500

⇒ P = ⁶⁵⁰⁰/_¹²⁵/100

⇒ P = 6500 × ¹⁰⁰/₁₂₅

⇒ P = ^{6500 × 100}/₁₂₅

⇒ P = ⁶⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $5200

Thus, the sum borrowed (P) = $5200 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6500, then the Principal = ¹⁰⁰/₁₂₅ × 6500

= ^{100 × 6500}/₁₂₅

= ⁶⁵⁰⁰⁰⁰/₁₂₅

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(8) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(10) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.