Simple Interest
Math MCQs

Question :    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) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(2) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

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

(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.