Simple Interest
Math MCQs

Question :    How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $6240

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

$6240 = P (1 + 4% × 5)

⇒ $6240 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6240 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6240 = P (1 + ²⁰/₁₀₀)

⇒ $6240 = P (^{100 + 20}/₁₀₀)

⇒ $6240 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6240

⇒ P = ⁶²⁴⁰/_¹²⁰/100

⇒ P = 6240 × ¹⁰⁰/₁₂₀

⇒ P = ^{6240 × 100}/₁₂₀

⇒ P = ⁶²⁴⁰⁰⁰/₁₂₀

⇒ 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 = 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 6240, then the Principal = ¹⁰⁰/₁₂₀ × 6240

= ^{100 × 6240}/₁₂₀

= ⁶²⁴⁰⁰⁰/₁₂₀

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.

(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

(8) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(10) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.