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) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.

(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(9) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.