Simple Interest
Math MCQs

Question :    Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4140

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4140 = P (1 + 5% × 3)

⇒ $4140 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4140 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4140 = P (1 + ¹⁵/₁₀₀)

⇒ $4140 = P (^{100 + 15}/₁₀₀)

⇒ $4140 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4140

⇒ P = ⁴¹⁴⁰/_¹¹⁵/100

⇒ P = 4140 × ¹⁰⁰/₁₁₅

⇒ P = ^{4140 × 100}/₁₁₅

⇒ P = ⁴¹⁴⁰⁰⁰/₁₁₅

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4140, then the Principal = ¹⁰⁰/₁₁₅ × 4140

= ^{100 × 4140}/₁₁₅

= ⁴¹⁴⁰⁰⁰/₁₁₅

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

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