Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $6440

Rate of Simple Interest (R) = 3%

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

$6440 = P (1 + 3% × 5)

⇒ $6440 = P (1 + ³/₁₀₀ × 5)

⇒ $6440 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6440 = P (1 + ¹⁵/₁₀₀)

⇒ $6440 = P (^{100 + 15}/₁₀₀)

⇒ $6440 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6440

⇒ P = ⁶⁴⁴⁰/_¹¹⁵/100

⇒ P = 6440 × ¹⁰⁰/₁₁₅

⇒ P = ^{6440 × 100}/₁₁₅

⇒ P = ⁶⁴⁴⁰⁰⁰/₁₁₅

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6440, then the Principal = ¹⁰⁰/₁₁₅ × 6440

= ^{100 × 6440}/₁₁₅

= ⁶⁴⁴⁰⁰⁰/₁₁₅

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?

(4) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

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

(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.