Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $6720

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

$6720 = P (1 + 4% × 5)

⇒ $6720 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6720 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6720 = P (1 + ²⁰/₁₀₀)

⇒ $6720 = P (^{100 + 20}/₁₀₀)

⇒ $6720 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6720

⇒ P = ⁶⁷²⁰/_¹²⁰/100

⇒ P = 6720 × ¹⁰⁰/₁₂₀

⇒ P = ^{6720 × 100}/₁₂₀

⇒ P = ⁶⁷²⁰⁰⁰/₁₂₀

⇒ P = $5600

Thus, the sum borrowed (P) = $5600 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 6720, then the Principal = ¹⁰⁰/₁₂₀ × 6720

= ^{100 × 6720}/₁₂₀

= ⁶⁷²⁰⁰⁰/₁₂₀

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(3) 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.

(4) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(10) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.