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) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?

(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.