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) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(4) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.