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) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(3) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.

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

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.