Simple Interest
Math MCQs

Question :    Donald had to pay $5175 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  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5175

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

$5175 = P (1 + 5% × 3)

⇒ $5175 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5175 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5175 = P (1 + ¹⁵/₁₀₀)

⇒ $5175 = P (^{100 + 15}/₁₀₀)

⇒ $5175 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5175

⇒ P = ⁵¹⁷⁵/_¹¹⁵/100

⇒ P = 5175 × ¹⁰⁰/₁₁₅

⇒ P = ^{5175 × 100}/₁₁₅

⇒ P = ⁵¹⁷⁵⁰⁰/₁₁₅

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 5175, then the Principal = ¹⁰⁰/₁₁₅ × 5175

= ^{100 × 5175}/₁₁₅

= ⁵¹⁷⁵⁰⁰/₁₁₅

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(5) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.

(7) 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?

(8) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.

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