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) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?

(5) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(9) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.