Simple Interest
Math MCQs

Question :    Matthew had to pay $4830 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  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4830

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

$4830 = P (1 + 5% × 3)

⇒ $4830 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4830 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4830 = P (1 + ¹⁵/₁₀₀)

⇒ $4830 = P (^{100 + 15}/₁₀₀)

⇒ $4830 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4830

⇒ P = ⁴⁸³⁰/_¹¹⁵/100

⇒ P = 4830 × ¹⁰⁰/₁₁₅

⇒ P = ^{4830 × 100}/₁₁₅

⇒ P = ⁴⁸³⁰⁰⁰/₁₁₅

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4830, then the Principal = ¹⁰⁰/₁₁₅ × 4830

= ^{100 × 4830}/₁₁₅

= ⁴⁸³⁰⁰⁰/₁₁₅

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.

(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(3) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(4) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(7) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.