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) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.

(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(4) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(6) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

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

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.