Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $7360

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

$7360 = P (1 + 3% × 5)

⇒ $7360 = P (1 + ³/₁₀₀ × 5)

⇒ $7360 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7360 = P (1 + ¹⁵/₁₀₀)

⇒ $7360 = P (^{100 + 15}/₁₀₀)

⇒ $7360 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7360

⇒ P = ⁷³⁶⁰/_¹¹⁵/100

⇒ P = 7360 × ¹⁰⁰/₁₁₅

⇒ P = ^{7360 × 100}/₁₁₅

⇒ P = ⁷³⁶⁰⁰⁰/₁₁₅

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 7360, then the Principal = ¹⁰⁰/₁₁₅ × 7360

= ^{100 × 7360}/₁₁₅

= ⁷³⁶⁰⁰⁰/₁₁₅

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.

(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

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

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.